The Evolution of Physics

v

l

The

Evolution
of Physics

THE GROWTH OF IDEAS
FROM EARLY CONCEPTS TO
RELATIVITY AND QUANTA

by

Albert Einstein
and Leopold Infeld

SIMON AND SCHUSTER
NEW YORK* 1942

ALL RIGHTS RESERVED

Copyright, 1938, Albert Einstein and Leopold Infeld
Published by Simon and Schuster, Inc.
Rockefeller Center

1230 Sixth Avenue, New York 20, N. Y.

TWELFTH PRINTING

Manufactured in the United States of America

Table of Contents

I. THE RISE OF THE MECHANICAL VIEW

The great mystery story 3

The first clew 5

Vectors 12

The riddle of motion 1 9

One clew remains 34

Is heat a substance? 38

The roller-coaster 47

The rate of exchange 51

The philosophical background 5 5

T he kinetic theory of matter 59

II. THE DECLINE OF THE MECHANICAL VIEW

The two electric fluids 7 1

The magnetic fluids 8 3

T he first serious difficulty 87

The velocity of light 94

Light as substance 97

The riddle of color 1 00

What is a wave? 104

The wave theory of light 1 1 o

Longitudinal or transverse light waves? 120

Ether and the mechanical view 123

III. FIELD, RELATIVITY

The field as representation 129

T he two pillars of the field theory 142

The reality of the field 1 48

Field and ether 156

The mechanical scaffold 1 60

vi Table of Contents

Ether and motion 172

Time, distance, relativity 186

Relativity and mechanics 203

The time-space continuum 210

General relativity 220

Outside and inside the elevator 22 6

Geometry and experiment 235

General relativity and its verification 249

Field and matter 255

IV. QUANTA

Continuity— discontinuity 263

Elementary quanta of matter and electricity 265

The quanta of light 272

Light spectra 280

The waves of matter 286

Probability waves 295

Physics and reality 310

List of Plates

PLATE I. facing

PAGE

Brownian movement 66

PLATE II.

Diffraction of light 1 1 8

PLATE III.

Spectral lines, diffraction of X rays and of
electronic waves 286

Acknowledgments

We wish to thank all those who have so kindly
helped us with the preparation of this book, in particu-
lar:

Professors A. G. Shenstone, Princeton, N. J., and
St. Loria, Lwow, Poland, for photographs on plate III.

I. N. Steinberg for his drawings.

Dr. M. Phillips for reading the manuscript and for
her very kind help.

A. E. and L. I.

)

Preface

Before you begin reading, you rightly expect some
simple questions to be answered. For what purpose has
this book been written? Who is the imaginary reader
for whom it is meant?

It is difficult to begin by answering these questions
clearly and convincingly. This would be much easier,
though quite superfluous, at the end of the book. We
find it simpler to say just what this book does not
intend to be. We have not written a textbook of
physics. Here is no systematic course in elementary
physical facts and theories. Our intention was rather to
sketch in broad outline the attempts of the human
mind to find a connection between the world of ideas
and the world of phenomena. We have tried to show
the active forces which compel science to invent ideas
corresponding to the reality of our world. But our
representation had to be simple. Through the maze of
facts and concepts we had to choose some highway
which seemed to us most characteristic and significant.
Facts and theories not reached by this road had to be
omitted. We were forced, by our general aim, to make
a definite choice of facts and ideas. The importance of
a problem should not be judged by the number of
pages devoted to it. Some essential lines of thought
have been left out, not because they seemed to us un-

IX

x Preface

important, but because they do not He along the road
we have chosen.

Whilst writing the book we had long discussions as
to the characteristics of our idealized reader and wor-
ried a good deal about him. We had him making up
for a complete lack of any concrete knowledge of
physics and mathematics by quite a great number of
virtues. We found him interested in physical and phil-
osophical ideas and we were forced to admire the pa-
tience with which he struggled through the less inter-
esting and more difficult passages. He realized that in
order to understand any page he must have read the
preceding ones carefully. He knew that a scientific
book, even though popular, must not be read in the
same way as a novel.

The book is a simple chat between you and us. You
may find it boring or interesting, dull or exciting, but
our aim will be accomplished if these pages give you
some idea of the eternal struggle of the inventive
human mind for a fuller understanding of the laws
governing physical phenomena.

■

I. THE RISE

OF THE MECHANICAL VIEW

The Rise of the Mechanical View

The great mystery story . . . The first clew . . . Vectors . . .
The riddle of motion . . . One clew remains ... Is heat a
substance? . . .The roller-coaster .. .The rate of exchange
.. .The philosophical background . . . The kinetic theory
of matter.

THE GREAT MYSTERY STORY

In imagination there exists the perfect mystery story.
Such a story presents all the essential clews, and com-
pels us to form our own theory of the case. If we
follow the plot carefully we arrive at the complete
solution for ourselves just before the author’s disclo-
sure at the end of the book. The solution itself, con-
trary to those of inferior mysteries, does not disap-
point us; moreover, it appears at the very moment we
expect it.

Can we liken the reader of such a book to the scien-
tists, who throughout successive generations continue
to seek solutions of the mysteries in the book of na-
ture? The comparison is false and will have to be aban-
doned later, but it has a modicum of justification which
may be extended and modified to make it more appro-
priate to the endeavor of science to solve the mystery
of the universe.

This great mystery story is still unsolved. We can-
not even be sure that it has a final solution. The read-

3

4 The Evolution of Physics

ing has already given us much; it has taught us the
rudiments of the language of nature; it has enabled us
to understand many of the clews, and has been a source
of joy and excitement in the oftentimes painful ad-
vance of science. But we realize that in spite of all the
volumes read and understood we are still far from a
complete solution, if, indeed, such a thing exists at all.
At every stage we try to find an explanation consistent
with the clews already discovered. Tentatively ac-
cepted theories have explained many of the facts, but
no general solution compatible with all known clews
has yet been evolved. Very often a seemingly perfect
theory has proved inadequate in the light of further
reading. New facts appear, contradicting the theory or
unexplained by it. The more we read, the more fully
do we appreciate the perfect construction of the book,
even though a complete solution seems to recede as we
advance.

In nearly every detective novel since the admirable
stories of Conan Doyle there comes a time where the
investigator has collected all the facts he needs for at
least some phase of his problem. These facts often seem
quite strange, incoherent, and wholly unrelated. The
great detective, however, realizes that no further inves-
tigation is needed at the moment, and that only pure
thinking will lead to a correlation of the facts col-
lected. So he plays his violin, or lounges in his arm-
chair enjoying a pipe, when suddenly, by Jove, he has
it! Not only does he have an explanation for the clews
at hand, but he knows that certain other events must

The Rise of the Mechanical View 5

have happened. Since he now knows exactly where to
look for it, he may go out, if he likes, to collect further
confirmation for his theory.

The scientist reading the book of nature, if we may
be allowed to repeat the trite phrase, must find the
solution for himself, for he cannot, as impatient readers
of other stories often do, turn to the end of the book.
In our case the reader is also the investigator, seeking
to explain, at least in part, the relation of events to
their rich context. To obtain even a partial solution the
scientist must collect the unordered facts available and
make them coherent and understandable by creative
thought.

It is our aim, in the following pages, to describe in
broad outline that work of physicists which corre-
sponds to the pure thinking of the investigator. We
shall be chiefly concerned with the role" of thoughts
and ideas in the adventurous search for knowledge of
the physical world.

THE FIRST CLEW

Attempts to read the great mystery story are as old
as human thought itself. Only a little over three hun-
dred years ago, however, did scientists begin to under-
stand the language of the story. Since that time, the age
of Galileo and Newton, the reading has proceeded
rapidly. Techniques of investigation, systematic meth-
ods of finding and following clews, have been devel-
oped. Some of the riddles of nature have been solved,

6

The Evolution of Physics

although many of the solutions have proved temporary
and superficial in the light of further research.

A most fundamental problem, for thousands of years
wholly obscured by its complications, is that of mo-
tion. All those motions we observe in nature, that of a
stone thrown into the air, a ship sailing the sea, a cart
pushed along the street, are in reality very intricate.
To understand these phenomena it is wise to begin
with the simplest possible cases, and proceed gradually
to the more complicated ones. Consider a body at rest,
where there is no motion at all. To change the position
of such a body it is necessary to exert some influence
upon it, to push it or lift it, or let other bodies, such as
horses or steam engines, act upon it. Our intuitive idea
is that motion is connected with the acts of pushing,
lifting or pulling. Repeated experience would make us
risk the further statement that we must push harder if
we wish to move the body faster. It seems natural to
conclude that the stronger the action exerted on a
body, the greater will be its speed. A four-horse car-
riage goes faster than a carriage drawn by only two
horses. Intuition thus tells us that speed is essentially
connected with action.

It is a familiar fact to readers of detective fiction
that a false clew muddles the story and postpones the
solution. The method of reasoning dictated by intui-
tion was wrong and led to false ideas of motion which
were held for centuries. Aristotle’s great authority
throughout Europe was perhaps the chief reason for

The Rise of the Mechanical View 7

the long belief in this intuitive idea. We read in the
Mechanics , for two thousand years attributed to him:

The moving body comes to a standstill when the force
which pushes it along can no longer so act as to push it.

The discovery and use of scientific reasoning by
Galileo was one of the most important achievements
in the history of human thought, and marks the real
beginning of physics. This discovery taught us that
intuitive conclusions based on immediate observation
are not always to be trusted, for they sometimes lead
to the wrong clews.

But where does intuition go wrong? Can it possibly
be wrong to say that a carriage drawn by four horses
must travel faster than one drawn by only two?

Let us examine the fundamental facts of motion
more closely, starting with simple everyday experi-
ences familiar to mankind since the beginning of .civ-
ilization and gained in the hard struggle for existence.

Suppose that someone going along a level road with
a pushcart suddenly stops pushing. The cart will go
on moving for a short distance before coming to rest.
We ask: how is it possible to increase this distance?
There are various ways, such as oiling the wheels, and
making the road very smooth. The more easily the
wheels turn, and the smoother the road, the longer the
cart will go on moving. And just what has been done
by the oiling and smoothing? Only this: the external
influences have been made smaller. The effect of what
is called friction has been diminished, both in the
wheels and between the wheels and the road. This is

8

The Evolution of Physics

already a theoretical interpretation of the observable
evidence, an interpretation which is, in fact, arbitrary.
One significant step further and we shall have the right
clew. Imagine a road perfectly smooth, and wheels
with no friction at all. Then there would be nothing
to stop the cart, so that it would run forever. This con-
clusion is reached only by thinking of an idealized ex-
periment, which can never be actually performed,
since it is impossible to eliminate all external influences.
The idealized experiment shows the clew which really
formed the foundation of the mechanics of motion.

Comparing the two methods of approaching the
problem we can say: the intuitive idea is — the
greater the action the greater the velocity. Thus the
velocity shows whether or not external forces are act-
ing on a body. The new clew found by Galileo is: if a
body is neither pushed, pulled, nor acted on in any
other way, or, more briefly, if no external forces act
on a body, it moves uniformly, that is, always with the
same velocity along a straight line. Thus, the velocity
does not show whether or not external forces are act-
ing on a body. Galileo’s conclusion, the correct one,
was formulated a generation later by Newton as the
Iww of inertia. It is usually the first thing about physics
which we learn by heart in school, and some of us may
remember it:

Every body perseveres in its state of rest, or of uniform
motion in a right line, unless it is compelled to change
that state by forces impressed thereon.

We have seen that this law of inertia cannot be de-

9

The Rise of the Mechanical View

rived directly from experiment, but only by specula-
tive thinking consistent with observation. The idealized
experiment can never be actually performed, although
it leads to a profound understanding of real experi-
ments.

From the variety of complex motions in the world
around us we choose as our first example uniform mo-
tion. This is the simplest, because there are no external
forces acting. Uniform motion can, however, never be
realized; a stone thrown from a tower, a cart pushed
along a road can never move absolutely uniformly be-
cause we cannot eliminate the influence of external
forces.

In a good mystery story the most obvious clews
often lead to the wrong suspects. In our attempts to
understand the laws of nature we find, similarly, that
the most obvious intuitive explanation is often the
wrong one.

Human thought creates an ever-changing picture of
the universe. Galileo’s contribution was to destroy the
intuitive view and replace it by a new one. This is the
significance of Galileo’s discovery.

But a further question concerning motion arises im-
mediately. If the velocity is no indication of the exter-
nal forces acting on a body, what is? The answer to
this fundamental question was found by Galileo and
still more concisely by Newton, and forms a further
clew in our investigation.

To find the correct answer we must think a little
more deeply about the cart on a perfectly smooth road.

IO The Evolution of Physics

In our idealized experiment the uniformity of the mo-
tion was due to the absence of all external forces. Let us
now imagine that the uniformly moving cart is given
a push in the direction of the motion. What happens
now? Obviously its speed is increased. Just as ob-
viously, a push in the direction opposite to that of the
motion would decrease the speed. In the first case the
cart is accelerated by the push, in the second case
decelerated, or slowed down. A conclusion follows at
once: the action of an external force changes the
velocity. Thus not the velocity itself but its change is
a consequence of pushing or pulling. Such a force
either increases or decreases the velocity according to
whether it acts in the direction of motion or in the
opposite direction. Galileo saw this clearly and wrote
in his Two New Sciences :

. . . any velocity once imparted to a moving body will
be rigidly maintained as long as the external causes of
acceleration or retardation are removed, a condition which
is found only on horizontal planes; for in the case of
planes which slope downwards there is already present a
cause of acceleration; while on planes sloping upward
there is retardation; from this it follows that motion alone
a horizontal plane is perpetual; for, if the velocity be uni-
form, it cannot be diminished or slackened, much less de-
stroyed.

By following the right clew we achieve a deeper
understanding of the problem of motion. The connec-
tion between force and the change of velocity and
not, as we should think according to our intuition, the
connection between force and the velocity itself is

The Rise of the Mechanical View n

the basis of classical mechanics as formulated by
Newton.

We have been making use of two concepts which
play principal roles in classical mechanics: force and
change of velocity. In the further development of
science both of these concepts are extended and gener-
alized. They must, therefore, be examined more closely.

What is force? Intuitively, we feel what is meant by
this term. The concept arose from the effort of push-
ing, throwing or pulling; from the muscular sensation
accompanying each of these acts. But its generalization
goes far beyond these simple examples. We can think
of force even without picturing a horse pulling a
carriage! We speak of the force of attraction between
the sun and the earth, the earth and the moon, and of
those forces which cause the tides. We speak of the
force by which the earth compels ourselves and all the
objects about us to remain within its sphere of in-
fluence, and of the force with which the wind makes
waves on the sea, or moves the leaves of trees. When
and where we observe a change in velocity, an external
force, in the general sense, must be held responsible.
Newton wrote in his Principia :

An impressed force is an action exerted upon a body,
in order to change its state, either of rest, or of moving
uniformly forward in a right line.

This force consists in the action only; and remains no
longer in the body, when the action is over. For a body
maintains every new state it acquires, by its vis inertiae
only. Impressed forces are of different origins; as from
percussion, from pressure, from centripetal force.

12

The Evolution of Physics

If a stone is dropped from the top of a tower its mo-
tion is by no means uniform; the velocity increases as
the stone falls. We conclude: an external force is act-
ing in the direction of the motion. Or, in other words:
the earth attracts the stone. Let us take another ex-
ample. What happens when a stone is thrown straight
upward? The velocity decreases until the stone reaches
its highest point and begins to fall. This decrease in
velocity is caused by the same force as the acceleration
of a falling body. In one case the force acts in the
direction of the motion, in the other case in the oppo-
site direction. The force is the same, but it causes ac-
celeration or deceleration according to whether the
stone is dropped or thrown upward.

VECTORS

All motions we have been considering are rectilinear ,
that is, along a straight line. Now we must go one step
further. We gain an understanding of the laws of na-
ture by analyzing the simplest cases and by leaving out
of our first attempts all intricate complications. A
straight line is simpler than a curve. It is, however, im-
possible to be satisfied with an understanding of recti-
linear motion alone. The motions of the moon, the
earth and the planets, just those to which the prin-
ciples of mechanics have been applied with such bril-
liant success, are motions along curved paths. Passing
from rectilinear motion to motion along a curved path
brings new difficulties. We must have the courage to
overcome them if we wish to understand the prin-

i3

The Rise of the Me chemical View

ciples of classical mechanics which gave us the first
clews and so formed the starting point for the develop-
ment of science.

Let us consider another idealized experiment, in
which a perfect sphere rolls uniformly on a smooth
table. We know that if the sphere is given a push, that
is, if an external force is applied, the velocity will be
changed. Now suppose that the direction of the blow
is not, as in the example of the cart, in the line of
motion, but in a quite different direction, say, perpen-
dicular to that line. What happens to the sphere?
Three stages of the motion can be distinguished: the
initial motion, the action of the force, and the final
motion after the force has ceased to act. According to
the law of inertia the velocities before and after the
action of the force are both perfectly uniform. But
there is a difference between the uniform motion be-
fore and after the action of the force: the direction is
changed. The initial path of the sphere and the direc-
tion of the force are perpendicular to each other. The
final motion will be along neither of these two lines,
but somewhere between them, nearer the direction of
the force if the blow is a hard one and the initial veloc-
ity small, nearer the original line of motion if the blow
is gentle and the initial velocity great. Our new con-
clusion, based on the law of inertia, is: in general the
action of an external force changes not only the speed
but also the direction of the motion. An understand-
ing of this fact prepares us for the generalization intro-
duced into physics by the concept of vectors.

14 The Evolution of Physics

We can continue to use our straightforward method
of reasoning. The starting point is again Galileo’s law
of inertia. We are still far from exhausting the conse-
quences of this valuable clew to the puzzle of motion.

Let us consider two spheres moving in different di-
rections on a smooth table. So as to have a definite
picture we may assume the two directions perpendicu-
lar to each other. Since there are no external forces
acting, the motions are perfectly uniform. Suppose,
further, that the speeds are equal, that is, both cover
the same distance in the same interval of time. But is it
correct to say that the two spheres have the same
velocity? The answer can be yes or no! If the speed-
ometers of two cars both show forty miles per hour
it is usual to say that they have the same speed or veloc-
ity, no matter in which direction they are traveling.
But science must create its own language, its own con-
cepts, for its own use. Scientific concepts often begin
with those used in ordinary language for the affairs of
everyday life, but they develop quite differently.
They are transformed and lose the ambiguity associ-
ated with them in ordinary language, gaining in rigor-
ousness so that they may be applied to scientific
thought.

From the physicist’s point of view it is advantageous
to say that the velocities of the two spheres moving in
different directions are different. Although purely a
matter of convention, it is more convenient to say that
four cars traveling away from the same traffic circle on
different roads do not have the same velocity even

i5

The Rise of the Mechanical View

though the speeds, as registered on the speedometers, are
all forty miles per hour. This differentiation between
speed and velocity illustrates how physics, starting
with a concept used in everyday life, changes it in a
way which proves fruitful in the further development
of science.

If a length is measured, the result is expressed as a
number of units. The length of a stick may be 3 ft.
7 in.; the weight of some object 2 lb. 3 oz.; a measured
time interval so many minutes or seconds. In each of
these cases the result of the measurement is expressed
by a number. A number alone is, however, insuffi-
cient for describing some physical concepts. The rec-
ognition of this fact marked a distinct advance in scien-
tific investigation. A direction as well as a number is
essential for the characterization of a velocity, for
example. Such a quantity, possessing both magnitude
and direction, is called a vector. A suitable symbol for

>r

1 6 The Evolution of Physics

it is an arrow. Velocity may be represented by an
arrow or, briefly speaking, by a vector whose length
in some chosen scale of units is a measure of the speed,
and whose direction is that of the motion.

If four cars diverge with equal speed from a traffic
circle, their velocities can be represented by four vec-
tors of the same length, as seen from our last drawing.
In the scale used one inch stands for 40 m.p.h. In this
way any velocity may be denoted by a vector, and
conversely, if the scale is known, one may ascertain the
velocity from such a vector diagram.

If two cars pass each other on the highway and their
speedometers both show 40 m.p.h. we characterize
their velocities by two different vectors with arrows
pointing in opposite directions. So also the arrows in-
dicating “uptown” and “downtown” subway trains

>

<

must point in opposite directions. But all trains mov-
ing uptown at different stations or on different ave-
nues with the same speed have the same velocity, which
may be represented by a single vector. There is noth-
ing about a vector to indicate which stations the train
passes or on which of the many parallel tracks it is
running. In other words, according to the accepted
convention, all such vectors, as drawn below, may be
regarded as equal; they lie along the same or parallel
lines, are of equal length, and finally, have arrows

The Rise of the Mechanical View

17

pointing in the same direction. The next figure shows
vectors all different, because they differ either in length

or direction, or both. The same four vectors may be
drawn in another way, in which they all diverge from

1 8 The Evolution of Physics

a common point. Since the starting point does not mat-
ter, these vectors can represent the velocities of four
cars moving away from the same traffic circle, or the
velocities of four cars in different parts of the country
traveling with the indicated speeds in the indicated
directions.

This vector representation may now be used to de-
scribe the facts previously discussed concerning recti-
linear motion. We talked of a cart, moving uniformly
in a straight line and receiving a push in the direction
of its motion which increases its velocity. Graphically
this may be represented by two vectors, a shorter one
denoting the velocity before the push and a longer one
in the same direction denoting the velocity after the

i > >

— 1

push. The meaning of the dotted vector is clear; it rep-
resents the change in velocity for which, as we know,
the push is responsible. For the case where the force is
directed against the motion, where the motion is
slowed down, the diagram is somewhat different.

l

Again the dotted vector corresponds to a change in ve-
locity, but in this case its direction is different. It is clear
that not only velocities themselves but also their
changes are vectors. But every change in velocity is

l 9

The Rise of the Mechanical View

due to the action of an external force; thus the force
must also be represented by a vector. In order to char-
acterize a force it is not sufficient to state how hard we
push the cart; we must also say in which direction we
push. The force, like the velocity or its change, must
be represented by a vector and not by a number alone.
Therefore: the external force is also a vector, and must
have the same direction as the change in velocity. In
the last two drawings the dotted vectors show the
direction of the force as truly as they indicate the
change in velocity.

Here the skeptic may remark that he sees no advan-
tage in the introduction of vectors. All that has been
accomplished is the translation of previously recog-
nized facts into an unfamiliar and complicated lan-
guage. At this stage it would indeed be difficult to
convince him that he is wrong. For the moment he is,
in fact, right. But we shall see that just this strange
language leads to an important generalization in which
vectors appear to be essential.

THE RIDDLE OF MOTION

So long as we deal only with motion along a straight
line we are far from understanding the motions ob-
served in nature. We must consider motions along
curved paths, and our next step is to determine the laws
governing such motions. This is no easy task. In the
case of rectilinear motion our concepts of velocity,
change of velocity, and force proved most useful. But
we do not immediately see how we can apply them to

20

The Evolution of Physics

motion along a curved path. It is indeed possible to
imagine that the old concepts are unsuited to the
description of general motion, and that new ones must
be created. Should we try to follow our old path, or
seek a new one?

The generalization of a concept is a process very
often used in science. A method of generalization is
not uniquely determined, for there are usually numer-
ous ways of carrying it out. One requirement, how-
ever, must be rigorously satisfied: any generalized con-
cept must reduce to the original one when the original
conditions are fulfilled.

We can best explain this by the example with which
we are now dealing. We can try to generalize the old
concepts of velocity, change of velocity and force for
the case of motion along a curved path. Technically,
when speaking of curves, we include straight lines.
The straight line is a special and trivial example of a
curve. If, therefore, velocity, change in velocity and
force are introduced for motion along a curved line,
then they are automatically introduced for motion
along a straight line. But this result must not contra-
dict those results previously obtained. If the curve be-
comes a straight line, all the generalized concepts must
reduce to the familiar ones describing rectilinear mo-
tion. But this restriction is not sufficient to determine
the generalization uniquely. It leaves open many pos-
sibilities. The history of science shows that the simplest
generalizations sometimes prove successful and some-
times not. We must first make a guess. In our case it is

21

The Rise of the Mechanical View

a simple matter to guess the right method of generaliza-
tion. The new concepts prove very successful and
help us to understand the motion of a thrown stone as
well as that of the planets.

And now just what do the words velocity, change in
velocity, and force mean in the general case of motion
along a curved line? Let us begin with velocity. Along
the curve a very small body is moving from left to

right. Such a small body is often called a particle. The
dot on the curve in our drawing shows the position of
the particle at some instant of time. What is the veloc-
ity corresponding to this time and position? Again
Galileo’s clew hints at a way of introducing the veloc-
ity. We must, once more, use our imagination and
think about an idealized experiment. The particle
moves along the curve, from left to right, under the
influence of external forces. Imagine that at a given
time and at the point indicated by the dot, all these
forces suddenly cease to act. Then, the motion must,
according to the law of inertia, be uniform. In practice
we can, of course, never completely free a body from
all external influences. We can only surmise “what
would happen if . . . ?” and judge the pertinence of
our guess by the conclusions which can be drawn from
it and by their agreement with experiment.

22

The Evolution of Physics

The vector in the next drawing indicates the guessed
direction of the uniform motion if all external forces

were to vanish. It is the direction of the so-called tan-
gent. Looking at a moving particle through a micro-
scope one sees a very small part of the curve, which
appears as a small segment. The tangent is its prolonga-
tion. Thus the vector drawn represents the velocity at
a given instant. The velocity vector lies on the tangent.
Its length represents the magnitude of the velocity,
or the speed as indicated, for instance, by the speedom-
eter of a car.

Our idealized experiment about destroying the mo-
tion in order to find the velocity vector must not be
taken too seriously. It only helps us to understand what
we should call the velocity vector and enables us to
determine it for a’ given instant at a given point.

In the next drawing, the velocity vectors for three
different positions of a particle moving along a curve

are shown. In this case not only the direction but the
magnitude of the velocity, as indicated by the length
of the vector, varies during the motion.

23

The Rise of the Mechanical View

Does this new concept of velocity satisfy the re-
quirement formulated for all generalizations? That is:
does it reduce to the familiar concept if the curve
becomes a straight line? Obviously it does. The tan-
gent to a straight line is the line itself. The velocity
vector lies in the line of the motion, just as in the case
of the moving cart or the rolling spheres.

The next step is the introduction of the change in
velocity of a particle moving along a curve. This also
may be done in various ways, from which we choose
the simplest and most convenient. The last drawing
showed several velocity vectors representing the mo-
tion at various points along the path. The first two of
these may be drawn again so that they have a common

starting point, as we have seen is possible with vectors.
The dotted vector, we call the change in velocity. Its
starting point is the end of the first vector and its end
point the end of the second vector. This definition of
the change in velocity may, at first sight, seem artificial
and meaningless. It becomes much clearer in the special
case in which vectors (i) and (2) have the same direc-
tion. This, of course, means going over to the case of
straight-line motion. If both vectors have the same
initial point the dotted vector again connects their end
points. The drawing is now identical with that on page

24 The Evolution of Physics

1 — > >

1 >

1 8, and the previous concept is regained as a special case
of the new one. We may remark that we had to sepa-
rate the two lines in our drawing since otherwise they
would coincide and be indistinguishable.

We now have to take the last step in our process of
generalization. It is the most important of all the
guesses we have had to make so far. The connection
between force and change in velocity has to be estab-
lished so that we can formulate the clew which will
enable us to understand the general problem of motion.

The clew to an explanation of motion along a
straight line was simple: external force is responsible
for change in velocity; the force vector has the same
direction as the change. And now what is to be re-
garded as the clew to curvilinear motion? Exactly the
same! The only difference is that change of velocity
has now a broader meaning than before. A glance at
the dotted vectors of the last two drawings shows this
point clearly. If the velocity is known for all points
along the curve, the direction of the force at any
point can be deduced at once. One must draw the ve-
locity vectors for two instants separated by a very
short time-interval and therefore corresponding to
positions very near each other. The vector from the
end point of the first to that of the second indicates
the direction of the acting force. But it is essential that

25

The Rise of the Mechanical View

the two velocity vectors should be separated only by a
“very short” time-interval. The rigorous analysis of
such words as “very near,” “very short” is far from
simple. Indeed it was this analysis which led Newton
and Leibnitz to the discovery of differential calculus.

It is a tedious and elaborate path which leads to the
generalization of Galileo’s clew. We cannot show here
how abundant and fruitful the consequences of this
generalization have proved. Its application leads to
simple and convincing explanations of many facts pre-
viously incoherent and misunderstood.

From the extremely rich variety of motions we shall
take only the simplest and apply to their explanation
the law just formulated.

A bullet shot from a gun, a stone thrown at an angle,
a stream of water emerging from a hose, all describe
familiar paths of the same type, the parabola. Imagine
a speedometer attached to a stone, for example, so
that its velocity vector may be drawn for any instant.

The result may well be that represented in the last
drawing. The direction of the force acting on the
stone is just that of the change in velocity, and we have
seen how it may be determined. The result, shown in
the next drawing, indicates that the force is vertical,

26

The Evolution of Physics

and directed downward. It is exactly the same as when
a stone is allowed to fall from the top of a tower. The
paths are quite different, as also are the velocities, but
the change in velocity has the same direction, that is,
toward the center of the earth.

A stone attached to the end of a string and swung
around in a horizontal plane moves in a circular path.

All the vectors in the diagram representing this mo-
tion have the same length if the speed is uniform.

Nevertheless, the velocity is not uniform, for the path
is not a straight line. Only in uniform, rectilinear mo-
tion are there no forces involved. Here, however, there

27

The Rise of the Mechanical View

are, and the velocity changes not in magnitude but in
direction. According to the law of motion there must
be some force responsible for this change, a force in
this case between the stone and the hand holding the
string. A further question arises immediately: in what
direction does the force act? Again a vector diagram
shows the answer. The velocity vectors for two very
near points are drawn, and the change of velocity

found. This last vector is seen to be directed along the
string toward the center of the circle, and is always
perpendicular to the velocity vector, or tangent. In
other words the hand exerts a force on the stone by
means of the string.

Very similar is the more important example of the
revolution of the moon around the earth. This may be
represented approximately as uniform circular mo-
tion. The force is directed toward the earth for the
same reason that it was directed toward the hand in
our former example. There is no string connecting the
earth and the moon, but we can imagine a line be-
tween the centers of the two bodies; the force lies
along this line and is directed toward the center of the
earth, just as the force on a stone thrown in the air or
dropped from a tower.

28

The Evolution of Physics

All that we have said concerning motion can be
summed up in a single sentence. Force and change of
velocity are vectors having the same direction. This is
the initial clew to the problem of motion, but it cer-
tainly does not suffice for a thorough explanation of all
motions observed. The transition from Aristotle’s line
of thought to that of Galileo formed a most important
cornerstone in the foundation of science. Once this
break was made, the line of further development was
clear. Our interest here lies in the first stages of devel-
opment, in following initial clews, in showing how new
physical concepts are born in the painful struggle with
old ideas. We are concerned only with pioneer work
in science, which consists of finding new and unex-
pected paths of development; with the adventures in
scientific thought which create an ever-changing pic-
ture of the universe. The initial and fundamental steps
are always of a revolutionary character. Scientific im-
agination finds old concepts too confining, and replaces
them by new ones. The continued development along
any line already initiated is more in the nature of evo-
lution, until the next turning point is reached when a
still newer field must be conquered. In order to under-
stand, however, what reasons and what difficulties
force a change in important concepts, we must know
not only the initial clews, but also the conclusions
which can be drawn.

One of the most important characteristics of modem
physics is that the conclusions drawn from initial clews
are not only qualitative but also quantitative. Let us

29

The Rise of the Mechanical View

again consider a stone dropped from a tower. We have
seen that its velocity increases as it falls, but we should
like to know much more. Just how great is this change?
And what is the position and the velocity of the stone
at any time after it begins to fall? We wish to be able
to predict events and to determine by experiment
whether observation confirms these predictions and
thus the initial assumptions.

To draw quantitative conclusions we must use the
language of mathematics. Most of the fundamental
ideas of science are essentially simple, and may, as a
rule, be expressed in a language comprehensible to
everyone. To follow up these ideas demands the
knowledge of a highly refined technique of investiga-
tion. Mathematics as a tool of reasoning is necessary if
we wish to draw conclusions which may be compared
with experiment. So long as we are concerned only
with fundamental physical ideas we may avoid the
language of mathematics. Since in these pages we do
this consistently, we must occasionally restrict our-
selves to quoting, without proof, some of the results
necessary for an understanding of important clews
arising in the further development. The price which
must be paid for abandoning the language of mathe-
matics is a loss in precision, and the necessity of some-
times quoting results without showing how they were
reached.

A very important example of motion is that of the
earth around the sun. It is known that the path is a
closed curve, called the ellipse. The construction of a

3 °

The Evolution of Physics

vector diagram of the change in velocity shows that
the force on the earth is directed toward the sun. But

this, after all, is scant information. We should like to
be able to predict the position of the earth and the
other planets for any arbitrary instant of time, we
should like to predict the date and duration of the
next solar eclipse and many other astronomical events.
It is possible to do these things, but not on the basis of
our initial clew alone, for it is now necessary to know
not only the direction of the force but also its absolute
value, its magnitude. It was Newton who made the in-
spired guess on this point. According to his law of
gravitation the force of attraction between two bodies
depends in a simple way on their distance from each
other. It becomes smaller when the distance increases.
To be specific it becomes 2X2 = 4 times smaller if
the distance is doubled, 3X3 = 9 times smaller if the
distance is made three times as great.

Thus we see that in the case of gravitational force
we have succeeded in expressing, in a simple way, the

The Rise of the Mechanical View 31

dependence of the force on the distance between the
moving bodies. We proceed similarly in all other cases
where forces of different kinds, for instance, electric,
magnetic, and the like, are acting. We try to use a sim-
ple expression for the force. Such an expression is justi-
fied only when the conclusions drawn from it are
confirmed by experiment.

But this knowledge of the gravitational force alone
is not sufficient for a description of the motion of the
planets. We have seen that vectors representing force
and change in velocity for any short interval of time
have the same direction, but we must follow Newton
one step further and assume a simple relation between
their lengths. Given all other conditions the same, that
is, the same moving body and changes considered over
equal time intervals, then, according to Newton, the
change of velocity is proportional to the force.

Thus just two complementary guesses are needed
for quantitative conclusions concerning the motion of
the planets. One is of a general character, stating the
connection between force and change in velocity. The
other is special, and states the exact dependence of the
particular kind of force involved on the distance be-
tween the bodies. The first is Newton’s general law of
motion, the second his law of gravitation. Together
they determine the motion. This can be made clear by
the following somewhat clumsy-sounding reasoning.
Suppose that at a given time the position and velocity
of a planet can be determined, and that the force is
known. Then, according to Newton’s laws we know

32

The Evolution of Physics

the change in velocity during a short time interval.
Knowing the initial velocity and its change, we can
find the velocity and position of the planet at the end
of the time interval. By a continued repetition of this
process the whole path of the motion may be traced
without further recourse to observational data. This is,
in principle, the way mechanics predicts the course of
a body in motion, but the method used here is hardly
practical. In practice such a step-by-step procedure
would be extremely tedious as well as inaccurate. For-
tunately, it is quite unnecessary; mathematics furnishes
a short cut, and makes possible precise description of
the motion in much less ink than we use for a single
sentence. The conclusions reached in this way can be
proved or disproved by observation.

The same kind of external force is recognized in the
motion of a stone falling through the air and in the
revolution of the moon in its orbit, namely, that of the
earth’s attraction for material bodies. Newton recog-
nized that the motions of falling stones, of the moon,
and of planets are only very special manifestations of a
universal gravitational force acting between any two
bodies. In simple cases the motion may be described
and predicted by the aid of mathematics. In remote
and extremely complicated cases, involving the action
of many bodies on each other, a mathematical descrip-
tion is not so simple, but the fundamental principles
are the same.

We find the conclusions, at which we arrived by
following our initial clews, realized in the motion of a

The Rise of the Mechanical View 33

thrown stone, in the motion of the moon, the earth,
and the planets.

It is really our whole system of guesses which is to
be either proved or disproved by experiment. No one
of the assumptions can be isolated for separate testing.
In the case of the planets moving around the sun it is
found that the system of mechanics works splendidly.
Nevertheless we can well imagine that another system,
based on different assumptions, might work just as
well.

Physical concepts are free creations of the human
mind, and are not, however it may seem, uniquely de-
termined by the external world. In our endeavor to
understand reality we are somewhat like a man trying
to understand the mechanism of a closed watch. He
sees the face and the moving hands, even hears its tick-
ing, but he has no way of opening the case. If he is
ingenious he may form some picture of a mechanism
which could be responsible for all the things he ob-
serves, but he may never be quite sure his picture is the
only one which could explain his observations. He will
never be able to compare his picture with the real
mechanism and he cannot even imagine the possibility
or the meaning of such a comparison. But he certainly
believes that, as his knowledge increases, his picture of
reality will become simpler and simpler and will explain
a wider and wider range of his sensuous impressions.
He may also believe in the existence of the ideal limit
of knowledge and that it is approached by the human
mind. He may call this ideal limit the objective truth.

34

The Evolution of Physics

ONE CLEW REMAINS

When first studying mechanics one has the impres-
sion that everything in this branch of science is simple,
fundamental and settled for all time. One would hardly
suspect the existence of an important clew which no
one noticed for three hundred years. The neglected
clew is connected with one of the fundamental con-
cepts of mechanics, that of mass.

Again we return to the simple idealized experiment
of the cart on a perfectly smooth road. If the cart is
initially at rest and then given a push, it afterwards
moves uniformly with a certain velocity. Suppose that
the action of the force can be repeated as many times
as desired, the mechanism of pushing acting in the
same way and exerting the same force on the same
cart. However many times the experiment is repeated
the final velocity is always the same. But what happens
if the experiment is changed, if previously the cart was
empty and now it is loaded? The loaded cart will have
a smaller final velocity than the empty one. The con-
clusion is: if the same force acts on two different
bodies, both initially at rest, the resulting velocities will
not be the same. We say that the velocity depends on
the mass of the body, being smaller if the mass is
greater.

We know, therefore, at least in theory, how to de-
termine the mass of a body or, more exactly, how
many times greater one mass is than another. We have
identical forces acting on two resting masses. Finding

-

The Rise of the Mechanical View 35

that the velocity of the first mass is three times greater
than that of the second we conclude that the first mass
is three times smaller than the second. This is certainly
not a very practical way of determining the ratio of
two masses. We can, nevertheless, well imagine having
done it in this, or in some similar way, based upon the
application of the law of inertia.

How do we really determine mass in practice? Not,
of course, in the way just described. Everyone knows
the correct answer. We do it by weighing on a scale.

Let us discuss in more detail the two different ways
of determining mass.

The first experiment had nothing whatever to do
with gravity, the attraction of the earth. The cart
moves along a perfectly smooth and horizontal plane
after the push. Gravitational force, which causes the
cart to stay on the plane, does not change, and plays no
role in the determination of the mass. It is quite differ-
ent with weighing. We could never use a scale if the
earth did not attract bodies, if gravity did not exist.
The difference between the two determinations of
mass is that the first has nothing to do with the force
of gravity while the second is based essentially on its
existence.

We ask: if we determine the ratio of two masses in
both ways described above do we obtain the same re-
sult? The answer given by experiment is quite clear.
The results are exactly the same! This conclusion could
not have been foreseen, and is based on observation,
not reason. Let us, for the sake of simplicity, call the

3 6 The Evolution of Physics

mass determined in the first way the inertial mass and
that determined in the second way the gravitational
mass. In our world it happens that they are equal but
we can well imagine that this should not have been the
case at all. Another question arises immediately: is this
identity of the two kinds of mass purely accidental, or
does it have a deeper significance? The answer, from
the point of view of classical physics, is: the identity of
the two masses is accidental and no deeper significance
should be attached to it. The answer of modern physics
is just the opposite: the identity of the two masses is
fundamental and forms a new and essential clew lead-
ing to a more profound understanding. This was, in
fact, one of the most important clews from which the
so-called general theory of relativity was developed.

A mystery story seems inferior if it explains strange
events as accidents. It is certainly more satisfying to
have the story follow a rational pattern. In exactly the
same way a theory which offers an explanation for the
identity of gravitational and inertial mass is superior to
one which interprets their identity as accidental, pro-
vided, of course, that the two theories are equally con-
sistent with observed facts.

Since this identity of inertial and gravitational mass
was fundamental for the formulation of the theory of
relativity we are justified in examining it a little more
closely here. What experiments prove convincingly
that the two masses are the same? The answer lies in
Galileo’s old experiment in which he dropped different
masses from a tower. He noticed that the time required

The Rise of the Mechanical View 37

for the fall was always the same, that the motion of a
falling body does not depend on the mass. To link this
simple but highly important experimental result with
the identity of the two masses needs some rather in-
tricate reasoning.

A body at rest gives way before the action of an ex-
ternal force, moving and attaining a certain velocity. It
yields more or less easily, according to its inertial mass,
resisting the motion more strongly if the mass is large
than if it is small. We may say, without pretending to
be rigorous: the readiness with which a body responds
to the call of an external force depends on its inertial
mass. If it were true that the earth attracts all bodies
with the same force, that of greatest inertial mass
would move more slowly in falling than any other. But
this is not the case: all bodies fall in the same way.
This means that the force by which the earth attracts
different masses must be different. Now the earth at-
tracts a stone with the force of gravity and knows
nothing about its inertial mass. The “calling” force of
the earth depends on the gravitational mass. The “an-
swering” motion of the stone depends on the inertial
mass. Since the “answering” motion is always the same
—all bodies dropped from the same height fall in the
same way— it must be deduced that gravitational mass
and inertial mass are equal.

More pedantically a physicist formulates the same
conclusion: the acceleration of a falling body increases
in proportion to its gravitational mass and decreases in
proportion to its inertial mass. Since all falling bodies

38 The Evolution of Physics

have the same constant acceleration, the two masses
must be equal.

In our great mystery story there are no problems
wholly solved and settled for all time. After three hun-
dred years we had to return to the initial problem of
motion, to revise the procedure of investigation, to
find clews which had been overlooked, thereby reach-
ing a different picture of the surrounding universe.

IS HEAT A SUBSTANCE?

Here we begin to follow a new clew, one originating
in the realm of heat phenomena. It is impossible, how-
ever, to divide science into separate and unrelated sec-
tions. Indeed, we shall soon find that the new concepts
introduced here are interwoven with those already fa-
miliar, and with those we shall still meet. A line of
thought developed in one branch of science can very
often be applied to the description of events apparently
quite different in character. In this process the original
concepts are often modified so as to advance the under-
standing both of those phenomena from which they
sprang and of those to which they are newly applied.

The most fundamental concepts in the description
of heat phenomena are temperature and heat. It took
an unbelievably long time in the history of science for
these two to be distinguished, but once this distinction
was made rapid progress resulted. Although these con-
cepts are now familiar to everyone we shall examine
them closely, emphasizing the differences between
them.

39

The Rise of the Mechanical View

Our sense of touch tells us quite definitely that one
body is hot and another cold. But this is a purely quali-
tative criterion, not sufficient for a quantitative descrip-
tion and sometimes even ambiguous. This is shown by
a well-known experiment: we have three vessels con-
taining, respectively, cold, warm and hot water. If we
dip one hand into the cold water and the other into the
hot, we receive a message from the first that it is cold
and from the second that it is hot. If we then dip both
hands into the same warm water we receive two con-
tradictory messages, one from each hand. For the same
reason an Eskimo and a native of some equatorial coun-
try meeting in New York on a spring day would hold
different opinions as to whether the climate was hot
or cold. We settle all such questions by the use of a
thermometer, an instrument designed in a primitive
form by Galileo. Here again that familiar name! The
use of a thermometer is based on some obvious physical
assumptions. We shall recall them by quoting a few
lines from lectures given about a hundred and fifty
years ago by Black, who contributed a great deal
toward clearing up the difficulties connected with the
two concepts, heat and temperature:

By the use of this instrument we have learned, that if
we take 1000, or more, different kinds of matter, such as
metals, stones, salts, woods, feathers, wool, water and a
variety of other fluids, although they be all at first of dif-
ferent heats, let them be placed together in the same room
without a fire, and into which the sun does not shine, the
heat will be communicated from the hotter of these bodies
to the colder, during some hours perhaps, or the course of

4° The Evolution of Physics

a day, at the end of which time, if we apply a thermom-
eter to them all in succession, it will point precisely to
the same degree.

The italicized word heats should, according to present-
day nomenclature, be replaced by the word tempera-
tures.

A physician taking the thermometer from a sick
man’s mouth might reason like this: “The thermometer
indicates its own temperature by the length of its col-
umn of mercury. We assume that the length of the
mercury column increases in proportion to the increase
in temperature. But the thermometer was for a few
minutes in contact with my patient, so that both pa-
tient and thermometer have the same temperature. I
conclude, therefore, that my patient’s temperature is
that registered on the thermometer.” The doctor prob-
ably acts mechanically, but he applies physical prin-
ciples without thinking about it.

But does the thermometer contain the same amount
of heat as the body of the man? Of course not. To as-
sume that two bodies contain equal quantities of heat
just because their temperatures are equal would, as
Black remarked, be

taking a very hasty view of the subject. It is confounding
the quantity of heat in different bodies with its general
strength or intensity, though it is plain that these are two
different things, and should always be distinguished, when
we are thinking of the distribution of heat.

An understanding of this distinction can be gained
by considering a very simple experiment. A pound of

The Rise of the Mechanical View 41

water placed over a gas flame takes some time to
change from room temperature to the boiling point. A
much longer time is required for heating twelve
pounds, say, of water in the same vessel by means of
the same flame. We interpret this fact as indicating that
now more of “something” is needed and we call this
“something”— heat.

A further important concept, specific heat, is gained
by the following experiment: let one vessel contain a
pound of water and another a pound of mercury, both
to be heated in the same way. The mercury gets hot
much more quickly than the water, showing that less
“heat” is needed to raise the temperature by one degree.
In general, different amounts of “heat” are required to
change by one degree, say from 40 to 41 degrees Fah-
renheit, the temperatures of different substances such
as water, mercury, iron, copper, wood, etc., all of the
same mass. We say that each substance has its individual
heat capacity , or specific heat.

Once having gained the concept of heat we can in-
vestigate its nature more closely. We have two bodies,
one hot, the other cold, or more precisely, one of a
higher temperature than the other. We bring them into
contact and free them from all other external in-
fluences. Eventually they will, we know, reach the
same temperature. But how does this take place? What
happens between the instant they are brought into
contact and the achievement of equal temperatures?
The picture of heat “flowing” from one body to an-
other suggests itself, like water flowing from a higher

42

The Evolution of Physics

level to a lower. This picture, though primitive, seems
to fit many of the facts, so that the analogy runs:

Water — Heat

Higher level — Higher temperature
Lower level — Lower temperature

The flow proceeds until both levels, that is, both tem-
peratures, are equal. This naive view can be made more
useful by quantitative considerations. If definite masses
of water and alcohol, each at a definite temperature,
are mixed together, a knowledge of the specific heats
will lead to a prediction of the final temperature of the
mixture. Conversely, an observation of the final tem-
perature, together with a little algebra, would enable
us to find the ratio of the two specific heats.

We recognize in the concept of heat which appears
here a similarity to other physical concepts. Heat is,
according to our view, a substance, such as mass in
mechanics. Its quantity may change or not, like money
put aside in a safe or spent. The amount of money in a
safe will remain unchanged so long as the safe remains
locked, and so will the amounts of mass and heat in an
isolated body. The ideal thermos bottle is analogous to
such a safe. Furthermore, just as the mass of an iso-
lated system is unchanged even if a chemical transfor-
mation takes place, so heat is conserved even though it
flows from one body to another. Even if heat is not
used for raising the temperature of a body but for
melting ice, say, or changing water into steam, we can
still think of it as a substance and regain it entirely by

43

The Rise of the Mechanical View

freezing the water or liquefying the steam. The old
names, latent heat of melting or vaporization, show
that these concepts are drawn from the picture of heat
as a substance. Latent heat is temporarily hidden, like
money put away in a safe, but available for use if one
knows the lock combination.

But heat is certainly not a substance in the same sense
as mass. Mass can be detected by means of scales, but
what of heat? Does a piece of iron weigh more when
red-hot than when ice-cold? Experiment shows that it
does not. If heat is a substance at all, it is a weightless
one. The “heat-substance” was usually called caloric
and is our first acquaintance among a whole family of
weightless substances. Later we shall have occasion to
follow the history of the family, its rise and fall. It is
sufficient now to note the birth of this particular mem-
ber.

The purpose of any physical theory is to explain as
wide a range of phenomena as possible. It is justified in
so far as it does make events understandable. We have
seen that the substance theory explains many of the
heat phenomena. It will soon become apparent, how-
ever, that this again is a false clew, that heat cannot be
regarded as a substance, even weightless. This is clear
if we think about some simple experiments which
marked the beginning of civilization.

We think of a substance as something which can be
neither created nor destroyed. Yet primitive man
created by friction sufficient heat to ignite wood. Ex-
amples of heating by friction are, as a matter of fact,

44 The Evolution of Physics

much too numerous and familiar to need recounting.
In all these cases some quantity of heat is created, a
fact difficult to account for by the substance theory. It
is true that a supporter of this theory could invent
arguments to account for it. His reasoning would run
something like this: “The substance theory can explain
the apparent creation of heat. Take the simplest exam-
ple of two pieces of wood rubbed one against the
other. Now rubbing is something which influences the
wood and changes its properties. It is very likely that
the properties are so modified that an unchanged quan-
tity of heat comes to produce a higher temperature
than before. After all, the only thing we notice is the
rise in temperature. It is possible that the friction
changes the specific heat of the wood and not the total
amount of heat.”

At this stage of the discussion it would be useless to
argue with a supporter of the substance theory, for this
is a matter which can be settled only by experiment.
Imagine two identical pieces of wood and suppose equal
changes of temperature are induced by different meth-
ods; in one case by friction and in the other by contact
with a radiator, for example. If the two pieces have the
same specific heat at the new temperature the whole
substance theory must break down. There are very
simple methods for determining specific heats, and the
fate of the theory depends on the result of just such
measurements. Tests which are capable of pronounc-
ing a verdict of life or death on a theory occur fre-
quently in the history of physics, and are called crucial

45

The Rise of the Mechanical View

experiments. The crucial value of an experiment is re-
vealed only by the way the question is formulated, and
only one theory of the phenomena can be put on trial
by it. The determination of the specific heats of two
bodies of the same kind, at equal temperatures attained
by friction and heat flow respectively, is a typical ex-
ample of a crucial experiment. This experiment was
performed about a hundred and fifty years ago by
Rumford, and dealt a death blow to the substance
theory of heat.

An extract from Rumford’s own account tells the
story:

It frequently happens, that in the ordinary affairs and
occupations of life, opportunities present themselves of
contemplating some of the most curious operations of Na-
ture; and very interesting philosophical experiments might
often be made, almost without trouble or expense, by
means of machinery contrived for the mere mechanical
purposes of the arts and manufactures.

I have frequendy had occasion to make this observation;
and am persuaded, that a habit of keeping the eyes open to
every thing that is going on in the ordinary course of the
business of life has oftener led, as it were by accident, or in
the playful excursions of the imagination, put into action
by contemplating the most common appearances, to use-
ful doubts, and sensible schemes for investigation and im-
provement, than all the more intense meditations of philos-
ophers, in the hours expressly set apart for study. . . .

Being engaged, lately, in superintending the boring of
cannon, in the workshops of the military arsenal at Munich,
I was struck with the very considerable degree of Heat
which a brass gun acquires, in a short time, in being bored;
and with the still more intense Heat (much greater than

46 The Evolution of Physics

that of boiling water, as I found by experiment) of the
metallic chips separated from it by the borer. . . .

From whence comes the Heat actually produced in the
mechanical operation above mentioned?

Is it furnished by the metallic chips which are sepa-
rated by the borer from the solid mass of metal?

If this were the case, then, according to the modern
doctrines of latent Heat, and of caloric, the capacity ought
not only to be changed, but the change undergone by
them should be sufficiently great to account for all the
Heat produced.

But no such change had taken place; for I found, upon
taking equal quantities, by weight, of these chips, and of
thin slips of the same block of metal separated by means
of a fine saw and putting them, at the same temperature
(that of boiling water), into equal quantities of cold water
(that is to say, at the temperature of 59/2 0 F.) the portion
of water into which the chips were put was not, to all
appearance, heated either less or more than the other por-
tion, in which the slips of metal were put.

Finally we reach his conclusion:

And, in reasoning on this subject, we must not forget
to consider that most remarkarble circumstance, that the
source of the Heat generated by friction, in these Experi-
ments, appeared evidently to be inexhaustible.

It is hardly necessary to add, that anything which any
insulated body, or system of bodies, can continue to fur-
nish without limitation, cannot possibly be a matexial sub-
stance-, and it appears to me to be extremely difficult, if
not quite impossible, to form any distinct idea of any-
thing, capable of being excited and communicated, in the
manner the Heat was excited and communicated in these
Experiments, except it be motion.

Thus we see the breakdown of the old theory, or to
be more exact, we see that the substance theory is lim-

The Rise of the Mechanical View 47

ited to problems of heat flow. Again, as Rumford has
intimated, we must seek a new clew. To do this, let us
leave for the moment the problem of heat and return
to mechanics.

THE ROLLER-COASTER

Let us trace the motion of that popular thrill-giver,
the roller-coaster. A small car is lifted or driven to the
highest point of the track. When set free it starts roll-
ing down under the force of gravity, and then goes up
and down along a fantastically curved line, giving the
occupants a thrill by the sudden changes in velocity.
Every roller-coaster has its highest point, that from
which it starts. Never again, throughout the whole
course of the motion will it reach the same height. A
complete description of the motion would be very
complicated. On the one hand is the mechanical side
of the problem, the changes of velocity and position in
time. On the other there is friction and therefore the
creation of heat, on the rail and in the wheels. The
only significant reason for dividing the physical proc-
ess into these two aspects is to make possible the use
of the concepts previously discussed. The division
leads to an idealized experiment, for a physical process
in which only the mechanical aspect appears can be
only imagined but never realized.

For the idealized experiment we may imagine that
someone has learned to eliminate entirely the friction
which always accompanies motion. He decides to ap-
ply his discovery to the construction of a roller-

48 The Evolution of Physics

coaster, and must find out for himself how to build
one. The car is to run up and down, with its starting
point, say, at one hundred feet above ground level. He
soon discovers by trial and error that he must follow a
very simple rule: he may build his track in whatever
path he pleases so long as no point is higher than the
starting point. If the car is to proceed freely to the

end of the course its height may attain a hundred feet
as many times as he likes, but never exceed it. The
initial height can never be reached by a car on an
actual track because of friction, but our hypothetical
engineer need not consider that.

Let us follow the motion of the idealized car on the
idealized roller-coaster as it begins to roll downward
from the starting point. As it moves its distance from
the ground diminishes, but its speed increases. This
sentence at first sight may remind us of one from a
language lesson: “I have no pencil, but you have six
oranges.” It is not so stupid, however. There is no
connection between my having no pencil and your
having ?ix oranges, but there is a very real correlation

The Rise of the Mechanical View 49

between the distance of the car from the ground and
its speed. We can calculate the speed of the car at any
moment if we know how high it happens to be above
the ground, but we omit this point here because of its
quantitative character which can best be expressed by
mathematical formulae.

At its highest point the car has zero velocity and is
one hundred feet from the ground. At the lowest pos-
sible point it is no distance from the ground, and has its
greatest velocity. These facts may be expressed in
other terms. At its highest point the car has potential
energy but no kinetic energy or energy of motion. At
its lowest point it has the greatest kinetic energy and
no potential energy whatever. At all intermediate posi-
tions, where there is some velocity and some elevation,
it has both kinetic and potential energy. The potential
energy increases with the elevation, while the kinetic
energy becomes greater as the velocity increases. The
principles of mechanics suffice to explain the motion.
Two expressions for energy occur in the mathematical
description, each of which changes, although the sum
does not vary. It is thus possible to introduce mathe-
matically and rigorously the concepts of potential en-
ergy, depending on position, and kinetic energy, de-
pending on velocity. The introduction of the two
names is, of course, arbitrary and justified only by
convenience. The sum of the two quantities remains
unchanged, and is called a constant of the motion. The
total energy, kinetic plus potential, is like a substance,
for example, money kept intact as to amount but

50 The Evolution of Physics

changed continually from one currency to another,
say from dollars to pounds and back again, according
to a well-defined rate of exchange.

In the real roller-coaster, where friction prevents the
car from again reaching as high a point as that from
which it started, there is still a continuous change be-
tween kinetic and potential energy. Here, however,
the sum does not remain constant, but grows smaller.

Now one important and courageous step more is
needed to relate the mechanical and heat aspects of
motion. The wealth of consequences and generaliza-
tions from this step will be seen later.

Something more than kinetic and potential energies
is now involved, namely, the heat created by friction.
Does this heat correspond to the diminution in me-
chanical energy, that is kinetic and potential energy?
A new guess is imminent. If heat may be regarded as a
form of energy, perhaps the sum of all three, heat,
kinetic and potential energies, remains constant. Not
heat alone, but heat and other forms of energy taken

The Rise of the Mechanical View 51

together are, like a substance, indestructible. It is as if
a man must pay himself a commission in francs for
changing dollars to pounds, the commission money also
being saved so that the sum of dollars, pounds, and
francs is a fixed amount according to some definite ex-
change rate.

The progress of science has destroyed the older con-
cept of heat as a substance. We try to create a new
substance, energy, with heat as one of its forms.

THE RATE OF EXCHANGE

Less than a hundred years ago the new clew which
led to the concept of heat as a form of energy was
guessed by Mayer and confirmed experimentally by
Joule. It is a strange coincidence that nearly all the
fundamental work concerned with the nature of heat
was done by non-professional physicists who regarded
physics merely as their great hobby. There was the
versatile Scotsman Black, the German physician
Mayer, and the great American adventurer Count
Rumford, who afterward lived in Europe, and among
other activities, became Minister of War for Bavaria.
There was also the English brewer Joule who, in his
spare time, performed some most important experi-
ments concerning the conservation of energy.

Joule verified by experiment the guess that heat is
a form of energy, and determined the rate of exchange.
It is worth our while to see just what his results were.

The kinetic and potential energy of a system to-
gether constitute its mechanical energy. In the case of

52

The Evolution of Physics

the roller-coaster we made a guess that some of the
mechanical energy was converted into heat. If this is
right there must be here and in all other similar physi-
cal processes a definite rate of exchange between the
two. This is rigorously a quantitative question, but the
fact that a given quantity of mechanical energy can be
changed into a definite amount of heat is highly im-
portant. We should like to know what number ex-
presses the rate of exchange, i.e. how much heat we
obtain from a given amount of mechanical energy.

The determination of this number was the object of
Joule’s researches. The mechanism of one of his experi-
ments is very much like that of a weight clock. The
winding of such a clock consists of elevating two
weights, thereby adding potential energy to the sys-
tem. If the clock is not further interfered with it may
be regarded as a closed system. Gradually the weights
fall and the clock runs. At the end of a certain time the
weights will have reached their lowest position and
the clock will have stopped. What has happened to
the energy? The potential energy of the weights has
changed into kinetic energy of the mechanism, and
has then gradually been dissipated as heat.

A clever alteration in this sort of mechanism enabled
Joule to measure the heat lost and thus the rate of
exchange. In his apparatus two weights caused a pad-
dle wheel to turn while immersed in water. The poten-
tial energy of the weights was changed into kinetic
energy of the movable parts, and thence into heat

The Rise of the Mechanical View

53

which raised the temperature of the water. Joule meas-
ured this change of temperature and, making use of
the known specific heat of water, calculated the
amount of heat absorbed. He summarized the results
of many trials as follows:

ist. That the quantity of heat produced by the friction
of bodies, whether solid or liquid, is always proportional
to the quantity of force [by force Joule means energy]
expended. And

2nd. That the quantity of heat capable of increasing
the temperature of a pound of water (weighed in vacuo
and taken at between 55 0 and 60 °) by i° Fahr. requires
for its evolution the expenditure of a mechanical force
[energy] represented by the fall of 772 lb. through the
space of one foot.

In other words the potential energy of 772 pounds
elevated one foot above the ground is equivalent to
the quantity of heat necessary to raise the temperature
of one pound of water from 55 0 F. to 56° F. Later
experimenters were capable of somewhat greater ac-

54

The Evolution of Thy sics

curacy, but the mechanical equivalent of heat is essen-
tially what Joule found in his pioneer work.

Once this important work was done, further prog-
ress was rapid. It was soon recognized that these kinds
of energy, mechanical and heat, are only two of its
many forms. Everything which can be converted into
either of them is also a form of energy. The radiation
given off by the sun is energy, for part of it is trans-
formed into heat on the earth. An electric current pos~
sesses energy, for it heats a wire or turns the wheels of
a motor. Coal represents chemical energy, liberated as
heat when the coal burns. In every event in nature one
form of energy is being converted into another, always
at some well-defined rate of exchange. In a closed sys-
tem, one isolated from external influences, the energy
is conserved and thus behaves like a substance. The
sum of all possible forms of energy in such a system is
constant, although the amount of any one kind may be
changing. If we regard the whole universe as a closed
system we can proudly announce with the physicists
of the nineteenth century that the energy of the uni-
verse is invariant, that no part of it can ever be created
or destroyed.

Our two concepts of substance are, then, matter and
energy. Both obey conservation laws: An isolated sys-
tem cannot change either in mass or in total energy.
Matter has weight but energy is weightless. We have
therefore two different concepts and two conservation
laws. Are these ideas still to be taken seriously? Or has
this apparently well-founded picture been changed in

The Rise of the Mechanical View 55

the light of newer developments? It has! Further
changes in the two concepts are connected with the
theory of relativity. We shall return to this point later.

THE PHILOSOPHICAL BACKGROUND

The results of scientific research very often force a
change in the philosophical view of problems which
extend far beyond the restricted domain of science it-
self. What is the aim of science? What is demanded of
a theory which attempts to describe nature? These
questions, although exceeding the bounds of physics,
are intimately related to it, since science forms the
material from which they arise. Philosophical gener-
alizations must be founded on scientific results. Once
formed and widely accepted, however, they very often
influence the further development of scientific thought
by indicating one of the many possible lines of pro-
cedure. Successful revolt against the accepted view
results in unexpected and completely different, devel-
opments, becoming a source of new philosophical as-
pects. These remarks necessarily sound vague and
pointless until illustrated by examples quoted from the
history of physics.

We shall here try to describe the first philosophical
ideas on the aim of science. These ideas greatly in-
fluenced the development of physics until nearly a
hundred years ago, when their discarding was forced
by new evidence, new facts and theories, which in
their turn formed a new background for science.

In the whole history of science from Greek philos-

5 The Evolution of Physics

ophy to modern physics there have been constant at-
tempts to reduce the apparent complexity of natural
phenomena to some simple fundamental ideas and rela-
tions. This is the underlying principle of all natural
philosophy. It is expressed even in the work of the
Atomists. Twenty-three centuries ago Democritus
wrote:

By convention sweet is sweet, by convention bitter is
bitter, by convention hot is hot, by convention cold is
cold, by convention color is color. But in reality there
are atoms and the void. That is, the objects of sense are
supposed to be real and it is customary to regard them
as such, but in truth they are not. Only the atoms and the
void are real.

This idea remains in ancient philosophy nothing
more than an ingenious figment of the imagination.
Laws of nature relating subsequent events were un-
known to the Greeks. Science connecting theory and
experiment really began with the work of Galileo. We
have followed the initial clews leading to the laws of
motion. Throughout two hundred years of scientific
research force and matter were the underlying con-
cepts in all endeavors to understand nature. It is impos-
sible to imagine one without the other because matter
demonstrates its existence as a source of force by its
action on other matter.

Let us consider the simplest example: two particles
with forces acting between them. The easiest forces to
imagine are those of attraction and repulsion. In both
cases the force vectors lie on a line connecting the ma-

57

The Rise of the Mechanical View

terial points. The demand for simplicity leads to the
picture of particles attracting or repelling each other;

Attraction

> <

• •

Repulsion

• < > •

any other assumption about the direction of the acting
forces would give a much more complicated picture.
Can we make an equally simple assumption about the
length of the force vectors? Even if we want to avoid
too special assumptions we can still say one thing: The
force between any two given particles depends only
on the distance between them, like gravitational forces.
This seems simple enough. Much more complicated
forces could be imagined, such as those which might
depend not only on the distance but also on the veloc-
ities of the two particles. With matter and force as our
fundamental concepts we can hardly imagine simpler
assumptions than that forces act along the line con-
necting the particles and depend only on the distance.
But is it possible to describe all physical phenomena by
forces of this kind alone?

The great achievements of mechanics in all its
branches, its striking success in the development of
astronomy, the application of its ideas to problems ap-
parently different and non-mechanical in character, all
these things contributed to the belief that it is possible

58 The Evolution of Physics

to describe all natural phenomena in terms of simple
forces between unalterable objects. Throughout the
two centuries following Galileo’s time such an en-
deavor, conscious or unconscious, is apparent in nearly
all scientific creation. This was clearly formulated by
Helmholtz about the middle of the nineteenth century:

Finally, therefore, we discover the problem of physical
material science to be to refer natural phenomena back to
unchangeable attractive and repulsive forces whose in-
tensity depends wholly upon distance. The solubility of
this problem is the condition of the complete compre-
hensibility of nature.

Thus, according to Helmholtz, the line of development
of science is determined and follows strictly a fixed
course:

And its vocation will be ended as soon as the reduction
of natural phenomena to simple forces is complete and
the proof given that this is the only reduction of which
the phenomena are capable.

This view appears dull and naive to a twentieth-
century physicist. It would frighten him to think that
the great adventure of research could be so soon fin-
ished, and an unexciting if infallible picture of the uni-
verse established for all time.

Although these tenets would reduce the description
of all events to simple forces, they do leave open the
question of just how the forces should depend on dis-
tance. It is possible that for different phenomena this
dependence is different. The necessity of introducing
many different kinds of force for different events is

59

The Rise of the Mechanical View

certainly unsatisfactory from a philosophical point of
view. Nevertheless this so-called mechanical view ,
most clearly formulated by Helmholtz, played an im-
portant role in its time. The development of the kinetic
theory of matter is one of the greatest achievements
directly influenced by the mechanical view.

Before witnessing its decline, let us provisionally ac-
cept the point of view held by the physicists of the
past century and see what conclusions we can draw
from their picture of the external world.

THE KINETIC THEORY OF MATTER

Is it possible to explain the phenomena of heat in
terms of the motions of particles interacting through
simple forces? A closed vessel contains a certain mass
of gas, air, for example, at a certain temperature. By
heating we raise the temperature, and thus increase the
energy. But how is this heat connected with motion?
The possibility of such a connection is suggested both
by our tentatively accepted philosophical point of
view and by the way in which heat is generated by
motion. Heat must be mechanical energy if every
problem is a mechanical one. The object of the kinetic
theory is to present the concept of matter just in this
way. According to this theory a gas is a congregation
of an enormous number of particles, or molecules ,
moving in all directions, colliding with each other and
changing in direction of motion with each collision.
There must exist an average speed of molecules, just as
in a large human community there exists an average

6o

The Evolution of Physics

age, or an average wealth. There will therefore be an
average kinetic energy per particle. More heat in the
vessel means a greater average kinetic energy. Thus
heat, according to this picture, is not a special form of
energy different from the mechanical one but is just
the kinetic energy of molecular motion. To any defi-
nite temperature there corresponds a definite average
kinetic energy per molecule. This is, in fact, not an
arbitrary assumption. We are forced to regard the
kinetic energy of a molecule as a measure of the tem-
perature of the gas if we wish to form a consistent me-
chanical picture of matter.

This theory is more than a play of the imagination.
It can be shown that the kinetic theory of gases is not
only in agreement with experiment, but actually leads
to a more profound understanding of the facts. This
may be illustrated by a few examples.

We have a vessel closed by a piston which can move
freely. The vessel contains a certain amount of gas to
be kept at a constant temperature. If the piston is ini-
tially at rest in some position it can be moved upward
by removing and downward by adding weight. To
push the piston down force must be used acting against
the inner pressure of the gas. What is the mechanism
of this inner pressure according to the kinetic theory?
A tremendous number of particles constituting the gas
are moving in all directions. They bombard the walls
and the piston, bouncing back like balls thrown against
a wall. This continual bombardment by a great number
of particles keeps the piston at a certain height by op-

The Rise of the Mechanical View 61

posing the force of gravity acting downward on the
piston and the weights. In one direction there is a con-
stant gravitational force, in the other very many irreg-
ular blows from the molecules. The net effect on the
piston of all these small irregular forces must be equal
to that of the force of gravity if there is to be equilib-
rium.

/ K Inner
Pressure

Gravitational

Force

Suppose the piston were pushed down so as to com-
press the gas to a fraction of its former volume, say
one-half, its temperature being kept unchanged. What,
according to the kinetic theory, can we expect to hap-
pen? Will the force due to the bombardment be more
or less effective than before? The particles are now
packed more closely. Although the average kinetic
energy is still the same, the collisions of the particles
with the piston will now occur more frequently and
thus the total force will be greater. It is clear from this
picture presented by the kinetic theory that to keep

6i

The Evolution of Physics

the piston in this lower position more weight is re-
quired. This simple experimental fact is well known,
but its prediction follows logically from the kinetic
view of matter.

Consider another experimental arrangement. Take
two vessels containing equal volumes of different gases,
say hydrogen and nitrogen, both at the same tempera-
ture. Assume the two vessels are closed with identical
pistons, on which are equal weights. This means,
briefly, that both gases have the same volume, tempera-
ture, and pressure. Since the temperature is the same,
so, according to the theory, is the average kinetic en-
ergy per particle. Since the pressures are equal, the two
pistons are bombarded with the same total force. On the
average every particle carries the same energy and both
vessels have the same volume. Therefore, the number
of molecules in each must be the same, although the
gases are chemically different. This result is very impor-
tant for the understanding of many chemical phenom-
ena. It means that the number of molecules in a given
volume, at a certain temperature and pressure, is some-
thing which is characteristic, not of a particular gas, but
of all gases. It is most astonishing that the kinetic theory
not only predicts the existence of such a universal num-
ber, but enables us to determine it. To this point we
shall return very soon.

The kinetic theory of matter explains quantitatively
as well as qualitatively the laws of gases as determined
by experiment. Furthermore, the theory is not re-

The Rise of the Mechanical View 6 3

stricted to gases, although its greatest successes have
been in this domain.

A gas can be liquefied by means of a decrease of tem-
perature. A fall in the temperature of matter means a
decrease in the average kinetic energy of its particles.
It is therefore clear that the average kinetic energy of
a liquid particle is smaller than that of a corresponding
gas particle.

A striking manifestation of the motion of particles
in liquids was given for the first time by the so-called
Brownian movement , a remarkable phenomenon which
would remain quite mysterious and incomprehensible
without the kinetic theory of matter. It was first ob-
served by the botanist Brown, and was explained
eighty years later, at the beginning of this century.
The only apparatus necessary for observing Brownian
motion is a microscope, which need not even be a par-
ticularly good one.

Brown was working with grains of pollen of certain
plants, that is:

particles or granules of unusually large size varying from
one four-thousandth to about five-thousandth of an inch
in length.

He reports further:

While examining the form of these particles immersed in
water, I observed many of them evidently in motion. . .
These motions were such as to satisfy me, after frequently
repeated observation, that they arose neither from cur-
rent in the fluid nor from its gradual evaporation, but
belonged to the particle itself.

6 4 The Evolution of Physics

What Brown observed was the unceasing agitation
of the granules when suspended in water and visible
through the microscope. It is an impressive sight!

Is the choice of particular plants essential for the
phenomenon? Brown answered this question by re-
peating the experiment with many different plants,
and found that all the granules, if sufficiently small,
showed such motion when suspended in water.
Furthermore, he found the same kind of restless, irreg-
ular motion in very small particles of inorganic as well
as organic substances. Even with a pulverized frag-
ment of a sphinx he observed the same phenomenon!

How is this motion to be explained? It seems con-
tradictory to all previous experience. Examination of
the position of one suspended particle, say every thirty
seconds, reveals the fantastic form of its path. The
amazing thing is the apparently eternal character of
the motion. A swinging pendulum placed in water
soon comes to rest if not impelled by some external
force. The existence of a never diminishing motion
seems contrary to all experience. This difficulty was
splendidly clarified by the kinetic theory of matter.

Looking at water through even our most powerful
microscopes we cannot see molecules and their motion
as pictured by the kinetic theory of matter. It must be
concluded that if the theory of water as a congrega-
tion of particles is correct, the size of the particles must
be beyond the limit of visibility of the best micro-
scopes. Let us nevertheless stick to the theory and as-
sume that it represents a consistent picture of reality.

The Rise of the Mechanical View 6 5

The Brownian particles visible through a microscope
are bombarded by the smaller ones composing the
water itself. The Brownian movement exists if the bom-
barded particles are sufficiently small. It exists because
this bombardment is not uniform from all sides and
cannot be averaged out, owing to its irregular and
haphazard character. The observed motion is thus the
result of the unobservable one. The behavior of the
big particles reflects in some way that of the molecules,
constituting, so to speak, a magnification so high that
it becomes visible through the microscope. The irregu-
lar and haphazard character of the path of the Brownian
particles reflects a similar irregularity in the path of
the smaller particles which constitute matter. We can
understand, therefore, that a quantitative study of
Brownian movement can give us deeper insight into
the kinetic theory of matter. It is apparent that the
visible Brownian motion depends on the size of the
invisible bombarding molecules. There would be no
Brownian motion at all if the bombarding molecules
did not possess a certain amount of energy or, in other
words, if they did not have mass and velocity. That
the study of Brownian motion can lead to a determina-
tion of the mass of a molecule is therefore not as-
tonishing.

Through laborious research, both theoretical and
experimental, the quantitative features of the kinetic
theory were formed. The clew originating in the phe-
nomenon of Brownian movement was one of those

66

The Evolution of Physics

which led to the quantitative data. The same data can
be obtained in different ways, starting from quite dif-
ferent clews. The fact that all these methods support
the same view is most important, for it demonstrates
the internal consistency of the kinetic theory of
matter.

Only one of the many quantitative results reached
by experiment and theory will be mentioned here. Sup-
pose we have a gram of the lightest of all elements, hy-
drogen, and ask: how many particles are there in this
one gram? The answer will characterize not only hy-
drogen but also all other gases, for we already know
under what conditions two gases have the same number
of particles.

The theory enables us to answer this question from
certain measurements of the Brownian motion of a
suspended particle. The answer is an astonishingly
great number: a three followed by twenty-three other
digits! The number of molecules in one gram of hydro-
gen is

303 ,000,000,000,000,000,000,000.

Imagine the molecules of a gram of hydrogen so in-
creased in size that they are visible through a micro-
scope, say that the diameter becomes one five-thou-
sandth of an inch, such as that of a Brownian particle.
Then, to pack them closely, we should have to use a
box each side of which is about one-quarter of a mile
long!

We can easily calculate the mass of one such hy-

PLATE I

(fbotograpbed by j. berrm)
Brownian particles seen through a microscope.

( Photographed by Brumberg and Vavilov )
One Brownian particle photo-
graphed by a long exposure and
covering a surface.

Consecutive posi-
tions observed for
one of the Brown-
ian particles.

The path averaged
from these consec-
utive positions.

The Rise of the Mechanical View 67

drogen molecule by dividing 1 by the number quoted
above. The answer is a fantastically small number:

0.000 000 000 000 000 000 000 0033 grams,

representing the mass of one molecule of hydrogen.

The experiments on Brownian motion are only some
of the many independent experiments leading to the
determination of this number which plays such an im-
portant part in physics.

In the kinetic theory of matter and in all its impor-
tant achievements we see the realization of the general
philosophical program: to reduce the explanation of
all phenomena to the interaction between particles of
matter.

We Summarize:

In mechanics the future path of a moving body can be
predicted and its past disclosed if its present condition and
the forces acting upon it are known. Thus, for example,
the future paths of all planets can be foreseen. The active
forces are Newton's gravitational forces depending on the
distance alone. The great results of classical mechanics
suggest that the mechanical view can be consistently ap-
plied to all branches of physics, that all phenomena can be
explained by the action of forces representing either at-
traction or repulsion, depending only upon distance and
acting between unchangeable particles.

In the kinetic theory of matter we see how this view,
arising from mechanical problems, embraces the phenom-
ena of heat and how it leads to a successful picture of the
structure of matter.

II. THE DECLINE
OF THE MECHANICAL VIEW

The Decline of the Mechanical View

The two electric fluids . ..The magnetic fluids . . . The
first serious difficulty .. .The velocity of light ... Light
as substance .. .The riddle of color . . . What is a wave?
...The wave theory of light ... Longitudinal or trans-
verse light waves? . . . Ether and the mechanical view

THE TWO ELECTRIC FLUIDS

The following pages contain a dull report of some
very simple experiments. The account will be boring
not only because the description of experiments is un-
interesting in comparison with their actual perform-
ance, but also because the meaning of the experiments
does not become apparent until theory makes it so.
Our purpose is to furnish a striking example of the
role of theory in physics.

i . A metal bar is supported on a glass base, and each
end of the bar is connected by means of a wire to an
electroscope. What is an electroscope? It is a simple
apparatus consisting essentially of two leaves of gold
foil hanging from the end of a short piece of metal.
This is enclosed in a glass jar or flask and the metal is
in contact only with non-metallic bodies, called insu-
lators. In addition to the electroscope and metal bar we
are equipped with a hard rubber rod and a piece of
flannel.

The experiment is performed as follows: we look

7 *

72

The Evolution of Physics

to see whether the leaves hang close together, for this
is their normal position. If by chance they do not, a
touch of the finger on the metal rod will bring them
together. These preliminary steps being taken, the

rubber rod is rubbed vigorously with the flannel and
brought into contact with the metal. The leaves sepa-
rate at once! They remain apart even after the rod is
removed.

2. We perform another experiment, using the same
apparatus as before, again starting with the gold leaves
hanging close together. This time we do not bring the
rubbed rod into actual contact with the metal, but
only near it. Again the leaves separate. But there is a
difference! When the rod is taken away without hav-
ing touched the metal, the leaves immediately fall back
to their normal position instead of remaining separated.

3. Let us change the apparatus slightly for a third
experiment. Suppose that the metal bar consists of two
pieces, joined together. We rub the rubber rod with

The Decline of the Mechanical View 73

flannel and again bring it near the metal. The same
phenomenon occurs, the leaves separate. But now let

us divide the metal rod into its two separate parts and
then take away the rubber rod. We notice that in this
case the leaves remain apart, instead of falling back to
their normal position as in the second experiment.

It is difficult to evince enthusiastic interest in these
simple and naive experiments. In the Middle Ages their
performer would probably have been condemned; to
us they seem both dull and illogical. It would be very
difficult to repeat them, after reading the account only
once, without becoming confused. Some notion of
the theory makes them understandable. We could say
more: it is hardly possible to imagine such experiments
performed as accidental play, without the pre-existence
of more or less definite ideas about their meaning.

We shall now point out the underlying ideas of a
very simple and naive theory which explains all the
facts described.

There exist two electric fluids , one called positive
(+) and the other negative (— ). They are somewhat
like substance in the sense already explained, in that
the amount can be enlarged or diminished, but the
total in any isolated system is preserved. There is, how-

74 The Evolution of Physics

ever, an essential difference between this case and that
of heat, matter or energy. We have two electrical sub-
stances. It is impossible here to use the previous anal-
ogy of money unless it is somehow generalized. A
body is electrically neutral if the positive and negative
electric fluids exactly cancel each other. A man has
nothing, either because he really has nothing, or be-
cause the amount of money put aside in his safe is
exactly equal to the sum of his debts. We can compare
the debit and credit entries in his ledger to the two
kinds of electric fluids.

The next assumption of the theory is that two elec-
tric fluids of the same kind repel each other, while
two of the opposite kind attract. This can be repre-
sented graphically in the following way:

A final theoretical assumption is necessary: There
are two kinds of bodies, those in which the fluids can
move freely, called conductors , and those in which
they cannot, called insulators. As is always true in
such cases, this division is not to be taken too seriously.
The ideal conductor or insulator is a fiction which can

The Decline of the Mechanical View 75

never be realized. Metals, the earth, the human body,
are all examples of conductors, although not equally
good. Glass, rubber, china, and the like are insulators.
Air is only partially an insulator as everyone who has
seen the described experiments knows. It is always a
good excuse to ascribe the bad results of electrostatic
experiments to the humidity of the air, which increases
its conductivity.

These theoretical assumptions are sufficient to ex-
plain the three experiments described. We shall dis-
cuss them once more, in the same order as before, but
in the light of the theory of electric fluids.

1. The rubber rod, like all other bodies under nor-
mal conditions, is electrically neutral. It contains the
two fluids, positive and negative, in equal amounts. By
rubbing with flannel we separate them. This statement
is pure convention, for it is the application of the ter-
minology created by the theory to the description of
the process of rubbing. The kind of electricity that the
rod has in excess afterwards is called negative, a name
which is certainly only a matter of convention. If the
experiments had been performed with a glass rod
rubbed with cat’s fur we should have had to call the
excess positive, to conform with the accepted conven-
tion. To proceed with the experiment, we bring elec-
tric fluid to the metal conductor by touching it with
the rubber. Here it moves freely, spreading over the
whole metal including the gold leaves. Since the action
of negative on negative is repulsion, the two leaves try
to get as far from each other as possible and the result is

7 <5 The Evolution of Thy sics

the observed separation. The metal rests on glass or
some other insulator so that the fluid remains on the
conductor, as long as the conductivity of the air per-
mits. We understand now why we have to touch the
metal before beginning the experiment. In this case the
metal, the human body, and the earth form one vast
conductor, with the electric fluid so diluted that prac-
tically nothing remains on the electroscope.

2. This experiment begins just in the same way as
the previous one. But instead of being allowed to touch
the metal the rubber is now only brought near it. The
two fluids in the conductor, being free to move, are
separated, one attracted and the other repelled. They
mix again when the rubber rod is removed, as fluids
of opposite kinds attract each other.

3. Now we separate the metal into two parts and
afterwards remove the rod. In this case the two fluids
cannot mix, so that the gold leaves retain an excess of
one electric fluid and remain apart.

In the light of this simple theory all the facts men-
tioned here seem comprehensible. The same theory does
more, enabling us to understand not only these, but
many other facts in the realm of “electrostatics.” The
aim of every theory is to guide us to new facts, sug-
gest new experiments, and lead to the discovery of new
phenomena and new laws. An example will make this
clear. Imagine a change in the second experiment. Sup-
pose I keep the rubber rod near the metal and at the
same time touch the conductor with my finger. What
will happen now? Theory answers: the repelled fluid

The Beeline of the Mechanical View 77

( — ) can now make its escape through my body, with
the result that only one fluid remains, the positive.

Only the leaves of the electroscope near the rubber
rod will remain apart. An actual experiment confirms
this prediction.

The theory with which we are dealing is certainly
naive and inadequate from the point of view of modern
physics. Nevertheless it is a good example showing the
characteristic features of every physical theory.

There are no eternal theories in science. It always
happens that some of the facts predicted by a theory
are disproved by experiment. Every theory has its
period of gradual development and triumph, after
which it may experience a rapid decline. The rise and
fall of the substance theory of heat, already discussed
here, is one of many possible examples. Others, more
profound and important, will be discussed later. Nearly
every great advance in science arises from a crisis
in the old theory, through an endeavor to find a
way out of the difficulties created. We must examine

7** The Evolution of Physics

old ideas, old theories, although they belong to the
past, for this is the only way to understand the impor-
tance of the new ones and the extent of their validity.

In the first pages of our book we compared the role
of an investigator to that of a detective who, after
gathering the requisite facts, finds the right solution
by pure thinking. In one essential this comparison must
be regarded as highly superficial. Both in life and in
detective novels the crime is given. The detective must
look for letters, fingerprints, bullets, guns, but at least
he knows that a murder has been committed. This is
not so for a scientist. It should not be difficult to
imagine someone who knows absolutely nothing about
electricity, since all the ancients lived happily enough
without any knowledge of it. Let this man be given
metal, gold foil, bottles, hard-rubber rod, flannel, in
short, all the material required for performing our
three experiments. He may be a very cultured person,
but he will probably put wine into the bottles, use the
flannel for cleaning, and never once entertain the idea
of doing the things we have described. For the detec-
tive the crime is given, the problem formulated: who
killed Cock Robin? The scientist must, at least in part,
commit his own crime, as well as carry out the investi-
gation. Moreover, his task is not to explain just one
case, but all phenomena which have happened or may
still happen. 1

In the introduction of the concept of fluids we see
the influence of those mechanical ideas which attempt
to explain everything by substances and simple forces

The Decline of the Mechanical View 79

acting between them. To see whether the mechanical
point of view can be applied to the description of elec-
trical phenomena, we must consider the following
problem. Two small spheres are given, both with an
electric charge, that is, both carrying an excess of one
electric fluid. We know that the spheres will either
attract or repel each other. But does the force depend
only on the distance, and if so, how? The simplest
guess seems to be that this force depends on the dis-
tance in the same way as gravitational force, which di-
minishes, say, to one-ninth of its former strength if the
distance is made three times as great. The experiments
performed by Coulomb showed that this law is really
valid. A hundred years after Newton discovered the
law of gravitation, Coulomb found a similar depend-
ence of electrical force on distance. The two major
differences between Newton’s law and Coulomb’s law
are: gravitational attraction is always present, while
electric forces exist only if the bodies possess electric
charges. In the gravitational case there is only attrac-
tion, but electric forces may either attract or repel.

There arises here the same question which we con-
sidered in connection with heat. Are the electrical
fluids weightless substances or not? In other words, is
the weight of a piece of metal the same whether neutral
or charged? Our scales show no difference. We con-
clude that the electric fluids are also members of the
family of weightless substances.

Further progress in the theory of electricity requires
the introduction of two new concepts. Again we shall

8o

The Evolution of Physics

avoid rigorous definitions, using instead analogies with
concepts already familiar. We remember how essential
it was for an understanding of the phenomena of heat
to distinguish between heat itself and temperature. It
is equally important here to distinguish between elec-
tric potential and electric charge. The difference be-
tween the two concepts is made clear by the analogy:

Electric potential — Temperature
Electric charge — Heat

Two conductors, for example two spheres of dif-
ferent size, may have the same electric charge, that is
the same excess of one electric fluid, but the potential
will be different in the two cases, being higher for the
smaller and lower for the larger sphere. The electric
fluid will have greater density and thus be more com-
pressed on the small conductor. Since the repulsive
forces must increase with the density, the tendency of
the charge to escape will be greater in the case of the
smaller sphere than in that of the larger. This tend-
ency of charge to escape from a conductor is a direct
measure of its potential. In order to show clearly the
difference between charge and potential we shall for-
mulate a few sentences describing the behavior of
heated bodies, and the corresponding sentences con-
cerning charged conductors.

Heat

Two bodies, initially at dif-
ferent temperatures, reach
the same temperature after

Electricity

Two insulated conductors,
initially at different electric
potentials, very quickly

The Decline of the Mechanical View 81

some time if brought into reach the same potential if
contact. brought into contact.

Equal quantities of heat
produce different changes
of temperature in two bod-
ies if their heat capacities
are different.

A thermometer in contact
with a body indicates— by
the length of its mercury
column— its own tempera-
ture and therefore the tem-
perature of the body.

Equal amounts of electric
charge produce different
changes of electric poten-
tial in two bodies if their
electrical capacities are dif-
ferent.

An electroscope in contact
with a conductor indicates
—by the separation of the
gold leaves— its own elec-
tric potential and therefore
the electric potential of the
conductor.

But this analogy must not be pushed too far. An ex-
ample shows the differences as well as the similarities.
If a hot body is brought into contact with a cold one,
the heat flows from the hotter to the colder. On the
other hand suppose that we have two insulated con-
ductors having equal but opposite charges, one positive
and the other negative. The two are at different poten-
tials. By convention we regard the potential corre-
sponding to a negative charge as lower than that cor-
responding to a positive charge. If the two conductors
are brought together or connected by a wire, it follows
from the theory of electric fluids that they will show
no charge and thus no difference of electric potential
at all. We must imagine a “flow” of electric charge
from one conductor to the other during the short time
in which the potential difference is equalized. But how?

82

The Evolution of Physics

Does the positive fluid flow to the negative body, or
the negative fluid to the positive body?

In the material presented here we have no basis for
deciding between these two alternatives. We can as-
sume either of the two possibilities, or that the flow is
simultaneous in both directions. It is only a matter of
adopting a convention, and no significance can be at-
tached to the choice, for we know no method of decid-
ing the question experimentally. Further development
leading to a much more profound theory of electricity
gave an answer to this problem, which is quite mean-
ingless when formulated in terms of the simple and
primitive theory of electric fluids. Here we shall simply
adopt the following mode of expression. The electric
fluid flows from the conductor having the higher po-
tential to that having the lower. In the case of our two
conductors the electricity thus flows from positive to

negative. This expression is only a matter of conven-
tion and is at this point quite arbitrary. The whole
difficulty indicates that the analogy between heat and
electricity is by no means complete.

We have seen the possibility of adapting the me-
chanical view to a description of the elementary facts
of electrostatics. The same is possible in the case of
magnetic phenomena.

The Decline of the Mechanical View 83

THE MAGNETIC FLUIDS

We shall proceed here in the same manner as before,
starting with very simple facts and then seeking their
theoretical explanation.

1. We have two long bar magnets, one suspended
freely at its center, the other held in the hand. The
ends of the two magnets are brought together in such
a way that a strong attraction is noticed between them.
This can always be done. If no attraction results we
must turn the magnet and try the other end. Some-
thing will happen if the bars are magnetized at all. The

ends of the magnets are called their poles. To continue
with the experiment we move the pole of the magnet
held in the hand along the other magnet. A decrease in
the attraction is noticed and when the pole reaches
the middle of the suspended magnet there is no evh
dence of any force at all. If the pole is moved further
in the same direction a repulsion is observed, attaining
its greatest strength at the second pole of the hanging
magnet.

2. The above experiment suggests another. Each

84 The Evolution of Thy sics

magnet has two poles. Can we not isolate one of them?
The idea is very simple: just break a magnet into two
equal parts. We have seen that there is no force be-
tween the pole of one magnet and the middle of the
other. But the result of actually breaking a magnet is
surprising and unexpected. If we repeat the experiment
described under (1), with only half a magnet sus-
pended, the results are exactly the same as before!
Where there was no trace of magnetic force previ-
ously, there is now a strong pole.

How are these facts to be explained? We can at-
tempt to pattern a theory of magnetism after the the-
ory of electric fluids. This is suggested by the fact that
here, as in electrostatic phenomena, we have attraction
and repulsion. Imagine two spherical conductors pos-
sessing equal charges, one positive and the other nega-
tive. Here “equal” means having the same absolute
value; +5 and —5, for example, have the same abso-
lute value. Let us assume that these spheres are con-
nected by means of an insulator such as a glass rod.

Schematically this arrangement can be represented by
an arrow directed from the negatively charged con-
ductor to the positive one. We shall call the whole
thing an electric dipole. It is clear that two such dipoles
would behave exactly like the bar magnets in experi-
ment ( 1 ) . If we think of our invention as a model for

The Decline of the Mechanical View 85

a real magnet, we may say, assuming the existence of
magnetic fluids, that a magnet is nothing but a mag-
netic dipole, having at its ends two fluids of different
kinds. This simple theory, imitating the theory of elec-
tricity, is adequate for an explanation of the first ex-
periment. There would be attraction at one end, repul-
sion at the other, and a balancing of equal and opposite
forces in the middle. But what of the second experi-
ment? By breaking the glass rod in the case of the
electric dipole we get two isolated poles. The same
ought to hold good for the iron bar of the magnetic
dipole, contrary to the results of the second experi-
ment. Thus this contradiction forces us to introduce a
somewhat more subtle theory. Instead of our previous
model we may imagine that the magnet consists of
very small elementary magnetic dipoles which cannot
be broken into separate poles. Order reigns in the mag-
net as a whole, for all the elementary dipoles are di-
rected in the same way. We see immediately why cut-

ting a magnet causes two new poles to appear on the
new ends, and why this more refined theory explains
the facts of experiment (1) as well as (2).

For many facts, the simpler theory gives an explana-
tion and the refinement seems unnecessary. Let us take
an example: We know that a magnet attracts pieces of

86 The Evolution of Physics

iron. Why? In a piece of ordinary iron the two mag-
netic fluids are mixed, so that no net effect results.
Bringing a positive pole near acts as a “command of
division” to the fluids, attracting the negative fluid of
the iron and repelling the positive. The attraction be-
tween iron and magnet follows. If the magnet is re-
moved, the fluids go back to more or less their original
state, depending on the extent to which they remember
the commanding voice of the external force.

Little need be said about the quantitative side of the
problem. With two very long magnetized rods we
could investigate the attraction (or repulsion) of their
poles when brought near one another. The effect of
the other ends of the rods is negligible if the rods are
long enough. How does the attraction or repulsion
depend on the distance between the poles? The answer
given by Coulomb’s experiment is that this dependence
on distance is the same as in Newton’s law of gravita-
tion and Coulomb’s law of electrostatics.

We see again in this theory the application of a gen-
eral point of view: the tendency to describe all phe-
nomena by means of attractive and repulsive forces
depending only on distance and acting between un-
changeable particles.

One well-known fact should be mentioned, for later
we shall make use of it. The earth is a great magnetic
dipole. There is not the slightest trace of an explana-
tion as to why this is true. The North Pole is approxi-
mately the minus (— ) and the South Pole the plus
(+) magnetic pole of the earth. The names plus and

The Decline of the Mechanical View 87

minus are only a matter of convention, but when once
fixed, enable us to designate poles in any other case. A
magnetic needle supported on a vertical axis obeys the
command of the magnetic force of the earth. It directs
its (+) pole toward the North Pole, that is, toward the
(— ) magnetic pole of the earth.

Although we can consistently carry out the mechan-
ical view in the domain of electric and magnetic phe-
nomena introduced here, there is no reason to be par-
ticularly proud or pleased about it. Some features of
the theory are certainly unsatisfactory if not discour-
aging. New kinds of substances had to be invented;
two electric fluids and the elementary magnetic dipoles.
The wealth of substances begins to be overwhelming!

The forces are simple. They are expressible in a
similar way for gravitational, electric, and magnetic
forces. But the price paid for this simplicity is high:
the introduction of new weightless substances. These
are rather artificial concepts, and quite unrelated to the
fundamental substance, mass.

THE FIRST SERIOUS DIFFICULTY

We are now ready to note the first grave difficulty
in the application of our general philosophical point of
view. It will be shown later that this difficulty, together
with another even more serious, caused a complete
breakdown of the belief that all phenomena can be ex-
plained mechanically.

The tremendous development of electricity as a
branch of science and technique began with the dis-

88

The Evolution of Physics

covery of the electric current. Here we find in the his-
tory of science one of the very few instances in which
accident seemed to play an essential role. The story of
the convulsion of a frog’s leg is told in many different
ways. Regardless of the truth concerning details, there
is no doubt that Galvani’s accidental discovery led
Volta at the end of the eighteenth century to the con-
struction of what is known as a voltaic battery. This is
no longer of any practical use, but it still furnishes a
very simple example of a source of current in school
demonstrations and in textbook descriptions.

The principle of its construction is simple. There are
several glass tumblers, each containing water with a
little sulphuric acid. In each glass two metal plates, one
copper and the other zinc, are immersed in the solu-
tion. The copper plate of one glass is connected to the
zinc of the next, so that only the zinc plate of the first
and the copper plate of the last glass remain uncon-
nected. We can detect a difference in electric potential
between the copper in the first glass and the zinc in the
last by means of a fairly sensitive electroscope if the
number of the “elements,” that is, glasses with plates,
constituting the battery, is sufficiently large.

It was only for the purpose of obtaining something
easily measurable with apparatus already described that
we introduced a battery consisting of several elements.
For further discussion, a single element will serve just
as well. The potential of the copper turns out to be
higher than that of the zinc. “Higher” is used here in
the sense in which +2 is greater than —2. If one con-

The Decline of the Mechanical View 89

ductor is connected to the free copper plate and an-
other to the zinc, both will become charged, the first
positively and the other negatively. Up to this point
nothing particularly new or striking has appeared, and
we may try to apply our previous ideas about potential
differences. We have seen that a potential difference be-
tween two conductors can be quickly nullified by
connecting them with a wire, so that there is a flow of
electric fluid from one conductor to the other. This
process was similar to the equalization of temperatures
by heat flow. But does this work in the case of a voltaic
battery? Volta wrote in his report that the plates be-
have like conductors:

. . . feebly charged, which act unceasingly or so that
their charge after each discharge reestablishes itself;
which, in a word, provides an unlimited charge or imposes
a perpetual action or impulsion of the electric fluid.

The astonishing result of his experiment is that the
potential difference between the copper and zinc plates
does not vanish as in the case of two charged conduc-
tors connected by a wire. The difference persists, and
according to the fluids theory it must cause a constant
flow of electric fluid from the higher potential level
(copper plate) to the lower (zinc plate). In an attempt
to save the fluid theory, we may assume that some con-
stant force acts to regenerate the potential difference
and cause a flow of electric fluid. But the whole phe-
nomenon is astonishing from the standpoint of energy.
A noticeable quantity of heat is generated in the wire
carrying the current, even enough to melt the wire if

90 The Evolution of Physics

it is a thin one. Therefore, heat-energy is created in the
wire. But the whole voltaic battery forms an isolated
system, since no external energy is being supplied. If
we want to save the law of conservation of energy we
must find where the transformations take place, and at
what expense the heat is created. It is not difficult to
realize that complicated chemical processes are taking
place in the battery, processes in which the immersed
copper and zinc, as well as the liquid itself, take active
parts. From the standpoint of energy this is the chain
of transformations which are taking place: chemical
energy — » energy of the flowing electric fluid, i.e., the
current -» heat. A voltaic battery does not last forever;
the chemical changes associated with the flow of elec-
tricity make the battery useless after a time.

The experiment which actually revealed the great
difficulties in applying the mechanical ideas must sound
strange to anyone hearing about it for the first time. It
was performed by Oersted about a hundred and
twenty years ago. He reports:

By these experiments it seems to be shown that the mag-
netic needle was moved from its position by help of a
galvanic apparatus, and that, when the galvanic circuit
was closed, but not when open, as certain very celebrated
physicists in vain attempted several years ago.

Suppose we have a voltaic battery and a conducting
wire. If the wire is connected to the copper plate but
not to the zinc, there will exist a potential difference
but no current can flow. Let us assume that the wire is
bent to form a circle, in the center of which a magnetic

The Decline of the Mechanical View 91

needle is placed, both wire and needle lying in the
same plane. Nothing happens as long as the wire does
not touch the zinc plate. There are no forces acting,
the existing potential difference having no influence

whatever on the position of the needle. It seems diffi-
cult to understand why the “very celebrated physi-
cists,” as Oersted called them, expected such an influ-
ence.

But now let us join the wire to the zinc plate.
Immediately a strange thing happens. The magnetic
needle turns from its previous position. One of its poles
now points to the reader if the page of this book repre-
sents the plane of the circle. The effect is that of a
force, perpendicular to the plane, acting on the mag-
netic pole. Faced with the facts of the experiment, we
can hardly avoid drawing such a conclusion about the
direction of the force acting.

This experiment is interesting, in the first place, be-

92

The Evolution of Physics

cause it shows a relation between two apparently quite
different phenomena, magnetism and electric current.
There is another aspect even more important. The
force between the magnetic pole and the small portions
of the wire through which the current flows cannot he
along lines connecting the wire and needle, or the
particles of flowing electric fluid and the elementary
magnetic dipoles. The force is perpendicular to these
lines! For the first time there appears a force quite
different from that to which, according to our mechan-
ical point of view, we intended to reduce all actions in
the external world. We remember that the forces of
gravitation, electrostatics, and magnetism, obeying the
laws of Newton and Coulomb, act along the line join-
ing the two attracting or repelling bodies.

This difficulty was stressed even more by an experi-
ment performed with great skill by Rowland nearly
sixty years ago. Leaving out technical details, this ex-
periment could be described as follows. Imagine a
small charged sphere. Imagine further that this sphere
moves very fast in a circle at the center of which is a
magnetic needle. This is, in principle, the same experi-
ment as Oersted’s, the only difference being that in-
stead of an ordinary current we have a mechanically
effected motion of the electric charge. Rowland found
that the result is indeed similar to that observed when
a current flows in a circular wire. The magnet is de-
flected by a perpendicular force.

Let us now move the charge faster. The force act-
ing on the magnetic pole is, as a result, increased; the

The Beeline of the Mechanical View 93

deflection from its initial position becomes more dis-
tinct. This observation presents another grave compli-

cation. Not only does the force fail to lie on the line
connecting charge and magnet, but the intensity of the
force depends on the velocity of the charge. The
whole mechanical point of view was based on the be-
lief that all phenomena can be explained in terms of
forces depending only on the distance and not on the
velocity. The result of Rowland’s experiment certainly
shakes this belief. Yet we may choose to be conserva-
tive and seek a solution within the frame of old ideas.

Difficulties of this kind, sudden and unexpected ob-
stacles in the triumphant development of a theory, arise
frequently in science. Sometimes a simple generaliza-
tion of the old ideas seems, at least temporarily, to be a
good way out. It would seem sufficient, in the present
case, for example, to broaden the previous point of
view and introduce more general forces between the
elementary particles. Very often, however, it is impos-
sible to patch up an old theory, and the difficulties re-

94 The Evolution of Physics

suit in its downfall and the rise of a new one. Here it
was not only the behavior of a tiny magnetic needle
which broke the apparently well-founded and success-
ful mechanical theories. Another attack, even more
vigorous, came from an entirely different angle. But
this is another story, and we shall tell it later.

THE VELOCITY OF LIGHT

In Galileo’s Two New Sciences, we listen to a con-
versation of the master and his pupils about the velocity
of light:

Sagredo: But of what kind and how great must we
consider this speed of light to be? Is it instantaneous or
momentary or does it, like other motion, require time?
Can we not decide this by experiment?

Simplicio: Everyday experience shows that the propa-
gation of light is instantaneous; for when we see a piece
of artillery fired, at great distance, the flash reaches our
eyes without lapse of time; but the sound reaches the ear
only after a noticeable interval.

Sagredo: Well, Simplicio, the only thing I am able to
infer from this familiar bit of experience is that sound, in
reaching our ears, travels more slowly than light; it does
not inform me whether the coming of the light is in-
stantaneous or whether, although extremely rapid, it still
occupies time. . . .

Salviati: The small conclusiveness of these and other
similar observations once led me to devise a method by
which one might accurately ascertain whether illumina-
tion, i.e., propagation of light, is really instantaneous. . . .

Salviati goes on to explain the method of his experi-
ment. In order to understand his idea let us imagine
that the velocity of light is not only finite, but also

The Decline of the Mechanical View 95

small, that the motion of light is slowed down, like that
in a slow-motion film. Two men, A and B, have cov-
ered lanterns and stand, say, at a distance of one mile
from each other. The first man, A, opens his lantern.
The two have made an agreement that B will open his
the moment he sees A’s light. Let us assume that in our
“slow motion” the light travels one mile in a second.
A sends a signal by uncovering his lantern. B sees it
after one second and sends an answering signal. This is
received by A two seconds after he had sent his own.
That is to say, if light travels with a speed of one mile
per second, then two seconds will elapse between A’s
sending and receiving a signal, assuming that B is a
mile away. Conversely, if A does not know the ve-
locity of light but assumes that his companion kept the
agreement, and he notices the opening of B’s lantern
two seconds after he opened his, he can conclude that
the speed of light is one mile per second.

With the experimental technique available at that
time Galileo had little chance of determining the ve-
locity of light in this way. If the distance were a mile,
he would have had to detect time intervals of the order
of one hundred-thousandth of a second!

Galileo formulated the problem of determining the
velocity of light, but did not solve it. The formulation
of a problem is often more essential than its solution,
which may be merely a matter of mathematical or ex-
perimental skill. To raise new questions, new possibili-
ties, to regard old problems from a new angle, requires
creative imagination and marks real advance in science.

96 The Evolution of Physics

The principle of inertia, the law of conservation of
energy were gained only by new and original thoughts
about already well-known experiments and phenom-
ena. Many instances of this kind will be found in the
following pages of this book, where the importance of
seeing known facts in a new light will be stressed and
new theories described.

Returning to the comparatively simple question of
determining the velocity of light, we may remark that
it is surprising that Galileo did not realize that his ex-
periment could be performed much more simply and
accurately by one man. Instead of stationing his com-
panion at a distance he could have mounted there a
mirror, which would automatically send back the sig-
nal immediately after receiving it.

About two hundred and fifty years later this very
principle was used by Fizeau, who was the first to de-
termine the velocity of light by terrestrial experiments.
It had been determined by Roemer much earlier,
though less accurately, by astronomical observation.

It is quite clear that in view of its enormous mag-
nitude, the velocity of light could be measured only
by taking distances comparable to that between the
earth and another planet of the solar system or by a
great refinement of experimental technique. The first
method was that of Roemer, the second that of Fizeau.
Since the days of these first experiments the very im-
portant number representing the velocity of light has
been determined many times, with increasing accuracy.
In our own century a highly refined technique was

The Decline of the Mechanical View 97

devised for this purpose by Michelson. The result of
these experiments can be expressed simply: The ve-
locity of light in vacuo is approximately 186,000 miles
per second, or 300,000 kilometers per second.

LIGHT AS SUBSTANCE

Again we start with a few experimental facts. The
number just quoted concerns the velocity of light in
vacuo. Undisturbed, light travels with this speed
through empty space. We can see through an empty
glass vessel if we extract the air from it. We see planets,
stars, nebulae, although the light travels from them to
our eyes through empty space. The simple fact that we
can see through a vessel whether or not there is air
inside shows us that the presence of air matters very
little. For this reason we can perform optical experi-
ments in an ordinary room with the same effect as if
there were no air.

One of the simplest optical facts is that the propaga-
tion of light is rectilinear. We shall describe a primitive
and naive experiment showing this. In front of a point
source is placed a screen with a hole in it. A point
source is a very small source of light, say, a small open-
ing in a closed lantern. On a distant wall the hole in
the screen will be represented as light on a dark back-
ground. The next drawing shows how this phenomenon
is connected with the rectilinear propagation of light.
All such phenomena, even the more complicated cases
in which light, shadow, and half -shadows appear, can

9 8 1 he Evolution of Physics

be explained by the assumption that light, in vacuo or
in air, travels along straight lines.

Let us take another example, a case in which light
passes through matter. We have a light beam traveling
through a vacuum and falling on a glass plate. What

happens? If the law of rectilinear motion were still
valid, the path would be that shown by the dotted line.
But actually it is not. There is a break in the path, such
as is shown in the drawing. What we observe here is
the phenomenon known as refraction. The familiar ap-

The Decline of the Mechanical View 99

pearance of a stick which seems to be bent in the mid-
dle if half-immersed in water is one of the many mani-
festations of refraction.

These facts are sufficient to indicate how a simple
mechanical theory of light could be devised. Our aim
here is to show how the ideas of substances, particles,
and forces penetrated the field of optics, and how
finally the old philosophical point of view broke down.

The theory here suggests itself in its simplest and
most primitive form. Let us assume that all lighted
bodies emit particles of light, or corpuscles , which, fall-
ing on our eyes, create the sensation of light. We are
already so accustomed to introduce new substances, if
necessary for a mechanical explanation, that we can do
it once more without any great hesitation. These cor^
puscles must travel along straight lines through empty
space with a known speed, bringing to our eyes mes-
sages from the bodies emitting light. All phenomena
exhibiting the rectilinear propagation of light support
the corpuscular theory, for just this kind of motion
was prescribed for the corpuscles. The theory also ex-
plains very simply the reflection of light by mirrors as
the same kind of reflection as that shown in the me-
chanical experiment of elastic balls thrown against a
wall, as the next drawing indicates.

The explanation of refraction is a little more diffi-
cult. Without going into details we can see the possi-
bility of a mechanical explanation. If corpuscles fall on
the surface of glass, for example, it may be that a force
is exerted on them by the particles of the matter, a

ioo The Evolution of Physics

force which strangely enough acts only in the immedi-
ate neighborhood of matter. Any force acting on a

moving particle changes the velocity, as we already
know. If the net force on the light-corpuscles is an
attraction perpendicular to the surface of the glass, the
new motion will lie somewhere between the line of the
original path and the perpendicular. This simple ex-
planation seems to promise success for the corpuscular
theory of light. To determine the usefulness and range
of validity of the theory, however, we must investigate
new and more complicated facts.

THE RIDDLE OF COLOR

It was again Newton’s genius which explained for
the first time the wealth of color in the world. Here is
a description of one of Newton’s experiments in his
own words:

In the year 1666 (at which time I applied myself to the
grinding of optick glasses of other figures than spherical)
I procured me a triangular glass prism, to try therewith
the celebrated phenomena of colours. And in order

The Decline of the Mechanical View ioi

thereto, having darkened my chamber, and made a small
hole in my window-shuts, to let in a convenient quantity
of the sun’s light, I placed my prism at its entrance, that it
might thereby be refracted to the opposite wall. It was at
first a very pleasing divertisement, to view the vivid and
intense colours produced thereby.

The light from the sun is “white.” After passing
through a prism it shows all the colors which exist in
the visible world. Nature herself reproduces the same
result in the beautiful color scheme of the rainbow. At-
tempts to explain this phenomenon are very old. The
Biblical story that a rainbow is God’s signature to a
covenant with man is, in a sense, a “theory.” But it
does not satisfactorily explain why the rainbow is re-
peated from time to time, and why always in connec-
tion with rain. The whole puzzle of color was first
scientifically attacked and the solution pointed out in
the great work of Newton.

One edge of the rainbow is always red and the other
violet. Between them all other colors are arranged.
Here is Newton’s explanation of this phenomenon:
every color is already present in white light. They all
traverse interplanetary space and the atmosphere in
unison and give the effect of white light. White light
is, so to speak, a mixture of corpuscles of different
kinds, belonging to different colors. In the case of
Newton’s experiment the prism separates them in
space. According to the mechanical theory, refraction
is due to forces acting on the particles of light and orig-
inating from the particles of glass. These forces are

102 The Evolution of Physics

different for corpuscles belonging to different colors,
being strongest for the violet and weakest for the red.
Each of the colors will therefore be refracted along a
different path and be separated from the others when
the light leaves the prism. In the case of a rainbow,
drops of water play the role of the prism.

The substance theory of light is now more com-
plicated than before. We have not one light substance
but many, each belonging to a different color. If, how-
ever, there is some truth in the theory, its consequences
must agree with observation.

The series of colors in the white light of the sun, as
revealed by Newton’s experiment, is called the spec-
trum of the sun, or more precisely, its visible spectrum.
The decomposition of white light into its components,
as described here, is called the dispersion of light. The
separated colors of the spectrum could be mixed to-
gether again by a second prism properly adjusted, un-
less the explanation given is wrong. The process should
be just the reverse of the previous one. We should ob-
tain white light from the previously separated colors.
Newton showed by experiment that it is indeed possi-
ble to obtain white light from its spectrum and the
spectrum from white light in this simple way as many
times as one pleases. These experiments formed a
strong support for the theory in which corpuscles be-
longing to each color behave as unchangeable sub-
stances. Newton wrote thus:

. . . which colours are not new generated, but only made
apparent by being parted; for if they be again entirely

The Decline of the Mechanical View 103

mixt and blended together, they will again compose that
colour, which they did before separation. And for the
same reason, transmutations made by the convening of
divers colours are not real; for when the difform rays are
again severed, they will exhibit the very same colours
which they did before they entered the composition; as
you see blue and yellow powders, when finely mixed, ap-
pear to the naked eye, green, and yet the colours of the
component corpuscles are not thereby really transmuted,
but only blended. For when viewed with a good micro-
scope they still appear blue and yellow interspersedly.

Suppose that we have isolated a very narrow strip of
the spectrum. This means that of all the many colors
we allow only one to pass through the slit, the others
being stopped by a screen. The beam which comes
through will consist of homogeneous light, that is, light
which cannot be split into further components. This is
a consequence of the theory and can be easily con-
firmed by experiment. In no way can such a beam of
single color be divided further. There are simple means
of obtaining sources of homogeneous light. For exam-
ple, sodium, when incandescent, emits homogeneous
yellow light. It is very often convenient to perform
certain optical experiments with homogeneous light,
since, as we can well understand, the result will be
much simpler.

Let us imagine that suddenly a very strange thing
happens: our sun begins to emit only homogeneous
light of some definite color, say yellow. The great va-
riety of colors on the earth would immediately vanish.
Everything would be either yellow or black! This pre-
diction is a consequence of the substance theory of

104 The Evolution of Physics

light, for new colors cannot be created. Its validity can
be confirmed by experiment: in a room where the only
source of light is incandescent sodium everything is
either yellow or black. The wealth of color in the
world reflects the variety of color of which white lig ht
is composed.

The substance theory of light seems to work splen-
didly in all these cases, although the necessity for in-
troducing as many substances as colors may make us
somewhat uneasy. The assumption that all the corpus-
cles of light have exactly the same velocity in empty
space also seems very artificial.

It is imaginable that another set of suppositions, a
theory of entirely different character, would work just
as well and give all the required explanations. Indeed,
we shall soon witness the rise of another theory, based
on entirely different concepts, yet explaining the same
domain of optical phenomena. Before formulating the
underlying assumptions of this new theory, however,
we must answer a question in no way connected with
these optical considerations. We must go back to me-
chanics and ask:

WHAT IS A WAVE?

A bit of gossip starting in Washington reaches New
York very quickly, even though not a single individual
who takes part in spreading it travels between these
two cities. There are two quite different motions in-
volved, that of the rumor, Washington to New York,
and that of the persons who spread the rumor. The

The Decline of the Mechanical View 105

wind, passing over a field of grain, sets up a wave
which spreads out across the whole field. Here again
we must distinguish between the motion of the wave
and the motion of the separate plants, which undergo
only small oscillations. We have all seen the waves that
spread in wider and wider circles when a stone is
thrown into a pool of water. The motion of the wave
is very different from that of the particles of water.
The particles merely go up and down. The observed
motion of the wave is that of a state of matter and not
of matter itself. A cork floating on the wave shows
this clearly, for it moves up and down in imitation of
the actual motion of the water, instead of being carried
along by the wave.

In order to understand better the mechanism of the
wave let us again consider an idealized experiment.
Suppose that a large space is filled quite uniformly with
water, or air, or some other “medium.” Somewhere in
the center there is a sphere. At the beginning of the
experiment there is no motion at all. Suddenly the
sphere begins to “breathe” rhythmically, expanding
and contracting in volume, although retaining its spher-
ical shape. What will happen in the medium? Let us
begin our examination at the moment the sphere begins
to expand. The particles of the medium in the immedi-
ate vicinity of the sphere are pushed out, so that the
density *of a spherical shell of water, or air, as the case
may be, is increased above its normal value. Similarly,
when the sphere contracts, the density of that part of
the medium immediately surrounding it will be de-

io 6 The Evolution of Physics

creased. These changes of density are propagated
throughout the entire medium. The particles constitut-
ing the medium perform only small vibrations, but the
whole motion is that of a progressive wave. The essen-
tially new thing here is that for the first time we con-
sider the motion of something which is not matter, but
energy propagated through matter.

Using the example of the pulsating sphere, we may
introduce two general physical concepts, important for
the characterization of waves. The first is the velocity
with which the wave spreads. This will depend on the
medium, being different for water and air, for exam-
ple. The second concept is that of wave-length. In the
case of waves on a sea or river it is the distance from
the trough of one wave to that of the next, or from the
crest of one wave to that of the next. Thus sea waves
have greater wave-length than river waves. In the
case of our waves set up by a pulsating sphere the
wave-length is the distance, at some definite time, be-
tween two neighboring spherical shells showing max-
ima or minima of density. It is evident that this dis-
tance will not depend on the medium alone. The rate
of pulsation of the sphere will certainly have a great
effect, making the wave-length shorter if the pulsation
becomes more rapid, longer if the pulsation becomes
slower.

This concept of a wave proved very successful in
physics. It is definitely a mechanical concept. The phe-
nomenon is reduced to the motion of particles which,
according to the kinetic theory, are constituents of

The Decline of the Mechanical View 107

matter. Thus every theory which uses the concept of
wave can, in general, be regarded as a mechanical
theory. For example, the explanation of acoustical phe-
nomena is based essentially on this concept. Vibrating
bodies, such as vocal cords and violin strings, are
sources of sound waves which are propagated through
the air in the manner explained for the pulsating sphere.
It is thus possible to reduce all acoustical phenomena to
mechanics by means of the wave concept.

It has been emphasized that we must distinguish be-
tween the motion of the particles and that of the wave
itself, which is a state of the medium. The two are
very different but it is apparent that in our example of
the pulsating sphere both motions take place in the

same straight line. The particles of the medium oscillate
along short line segments, and the density increases
and decreases periodically in accordance with this mo-

108 The Evolution of Physics

tion. The direction in which the wave spreads and the
line on which the oscillations lie are the same. This
type of wave is called longitudinal. But is this the only
kind of wave? It is important for our further considera-
tions to realize the possibility of a different kind of
wave, called transverse.

Let us change our previous example. We still have
the sphere, but it is immersed in a medium of a differ-
ent kind, a sort of jelly instead of air or water. Further-
more, the sphere no longer pulsates but rotates in one
direction through a small angle and then back again,

always in the same rhythmical way and about a definite
axis. The jelly adheres to the sphere and thus the ad-
hering portions are forced to imitate the motion. These
portions force those situated a little further away to
imitate the same motion, and so on, so that a wave is
set up in the medium. If we keep in mind the distinc-

The Decline of the Mechanical View 109

tion between the motion of the medium and the mo-
tion of the wave we see that here they do not lie on the
same line. The wave is propagated in the direction of
the radius of the sphere, while the parts of the medium
move perpendicularly to this direction. We have thus
created a transverse wave.

Waves spreading on the surface of water are trans-
verse. A floating cork only bobs up and down, but the
wave spreads along a horizontal plane. Sound waves,
on the other hand, furnish the most familiar example
of longitudinal waves.

One more remark: the wave produced by a pulsat-
ing or oscillating sphere in a homogeneous medium is
a spherical wave. It is called so because at any given
moment all points on any sphere surrounding the
source behave in the same way. Let us consider a por-
tion of such a sphere at a great distance from the
source. The farther away the portion is, and the
smaller we take it, the more it resembles a plane. We
can say, without trying to be too rigorous, that there
is no essential difference between a part of a plane and

no The Evolution of Physics

a part of a sphere whose radius is sufficiently large. We
very often speak of small portions of a spherical wave
far removed from the source as plane waves. The far-
ther we place the shaded portion of our drawing from
the center of the spheres and the smaller the angle be-
tween the two radii, the better our representation of a
plane wave. The concept of a plane wave, like many
other physical concepts, is no more than a fiction which
can be realized with only a certain degree of accuracy.
It is, however, a useful concept which we shall need
later.

THE WAVE THEORY OF LIGHT

Let us recall why we broke off the description of
optical phenomena. Our aim was to introduce another
theory of light, different from the corpuscular one, but
also attempting to explain the same domain of facts.
To do this we had to interrupt our story and introduce
the concept of waves. Now we can return to our sub-
ject.

It was Huygens, a contemporary of Newton, who
put forward a quite new theory. In his treatise on
light he wrote:

If, in addition, light takes time for its passage— which
we are now going to examine— it will follow that this
movement, impressed on the intervening matter, is suc-
cessive; and consequently it spreads, as sound does, by
spherical surfaces and waves, for I call them waves from
their resemblance to those which are seen to be formed
in water when a stone is thrown into it, and which present

Ill

The Decline of the Mechanical View

a successive spreading as circles, though these arise from
another cause, and are only in a flat surface.

According to Huygens, light is a wave, a transfer-
ence of energy and not of substance. We have seen
that the corpuscular theory explains many of the ob-
served facts. Is the wave theory also able to do this?
We must again ask the questions which have already
been answered by the corpuscular theory, to see
whether the wave theory can do the answering just as
well. We shall do this here in the form of a dialogue
between N and H, where N is a believer in Newton’s
corpuscular theory, and H in Huygen’s theory.
Neither is allowed to use arguments developed after
the work of the two great masters was finished.

N: In the corpuscular theory the velocity of light
has a very definite meaning. It is the velocity at which
the corpuscles travel through empty space. What does
it mean in the wave theory?

H: It means the velocity of the light wave, of course.
Every known wave spreads with some definite veloc-
ity, and so should a wave of light.

N: That is not as simple as it seems. Sound waves
spread in air, ocean waves in water. Every wave must
have a material medium in which it travels. But light
passes through a vacuum, whereas sound does not. To
assume a wave in empty space really means not to as-
sume any wave at all.

H: Yes, that is a difficulty, although not a new one
to me. My master thought about it very carefully, and
decided that the only way out is to assume the exist-

1 12 The Evolution of Physics

ence of a hypothetical substance, the ether, a trans-
parent medium permeating the entire universe. The
universe is, so to speak, immersed in ether. Once we
have the courage to introduce this concept, everything
else becomes clear and convincing.

N: But I object to such an assumption. In the first
place it introduces a new hypothetical substance, and
we already have too many substances in physics. There
is also another reason against it. You no doubt believe
that we must explain everything in terms of mechanics.
But what about the ether? Are you able to answer the
simple question as to how the ether is constructed from
its elementary particles and how it reveals itself in
other phenomena?

H: Your first objection is certainly justified. But by
introducing the somewhat artificial weightless ether we
at once get rid of the much more artificial light cor-
puscles. We have only one “mysterious” substance in-
stead of an infinite number of them corresponding to
the great number of colors in the spectrum. Do you
not think that this is real progress? At least all the
difficulties are concentrated on one point. We no
longer need the factitious assumption that particles be-
longing to different colors travel with the same speed
through empty space. Your second argument is also
true. We cannot give a mechanical explanation of
ether. But there is no doubt that the future study of
optical and perhaps other phenomena will reveal its
structure. At present we must wait for new experi-
ments and conclusions, but finally, I hope, we shall be

The Decline of the Mechanical View 113

able to clear up the problem of the mechanical struc-
ture of the ether.

N: Let us leave the question for the moment, since
it cannot be settled now. I should like to see how your
theory, even if we waive the difficulties, explains those
phenomena which are so clear and understandable in
the light of the corpuscular theory. Take, for example,
the fact that light rays travel in vacuo or in air along
straight lines. A piece of paper placed in front of a
candle produces a distinct and sharply outlined shadow
on the wall. Sharp shadows would not be possible if
the wave theory of light were correct, for waves would
bend around the edges of the paper and thus blur the
shadow. A small ship is not an obstacle for waves on
the sea, you know; they simply bend around it with-
out casting a shadow.

H: That is not a convincing argument. Take short
waves on a river impinging on the side of a large ship.
Waves originating on one side of the ship will not be
seen on the other. If the waves are small enough and
the ship large enough a very distinct shadow appears.
It is very probable that light seems to travel in straight
lines only because its wave-length is very small in com-
parison with the size of ordinary obstacles and of
apertures used in experiments. Possibly, if we could
create a sufficiently small obstruction, no shadow
would occur. We might meet with great experimental
difficulties in constructing apparatus which would
show whether light is capable of bending. Neverthe-
less, if such an experiment could be devised it would be

H4 The Evolution of Physics

crucial in deciding between the wave theory and the
corpuscular theory of light.

N: The wave theory may lead to new facts in the
future, but I do not know of any experimental data
confirming it convincingly. Until it is definitely proved
by experiment that light may be bent I do not see any
reason for not believing in the corpuscular theory,
which seems to me to be simpler, and therefore better,
than the wave theory.

At this point we may interrupt the dialogue, though
the subject is by no means exhausted.

It still remains to be shown how the wave theory
explains the refraction of light and the variety of col-
ors. The corpuscular theory is capable of this, as we
know. We shall begin with refraction, but it will be
useful to consider first an example having nothing to
do with optics.

There is a large open space in which there are walk-
ing two men holding between them a rigid pole. At
the beginning they are walking straight ahead, both
with the same velocity. As long as their velocities re-
main the same, whether great or small, the stick will
be undergoing parallel displacement; that is, it does not
turn or change its direction. All consecutive positions
of the pole are parallel to each other. But now imagine
that for a time which may be as short as a fraction of
a second the motions of the two men are not the same.
What will happen? It is clear that during this moment
the stick will turn, so that it will no longer be displaced
parallel to its original position. When the equal veloci-

The Decline of the Mechanical View 115

ties are resumed it is in a direction different from the
previous one. This is shown clearly in the drawing.

The change in direction took place during the time
interval in which the velocities of the two walkers
were different.

This example will enable us to understand the re-
fraction of a wave. A plane wave traveling through
the ether strikes a plate of glass. In the next drawing we
see a wave which presents a comparatively wide front
as it marches along. The wave front is a plane on which
at any given moment all parts of the ether behave in
precisely the same way. Since the velocity depends on
the medium through which the light is passing it will
be different in glass from the velocity in empty space.
During the very short time in which the wave front
enters the glass, different parts of the wave front will
have different velocities. It is clear that the part which
has reached the glass will travel with the velocity of
light in glass, while the other still moves with the ve-
locity of light in ether. Because of this difference in

ii 6 The Evolution of Physics

velocity along the wave front during the time of “im-
mersion” in the glass, the direction of the wave itself
will be changed.

Thus we see that not only the corpuscular theory,
but also the wave theory, leads to an explanation of re-
fraction. Further consideration, together with a little
mathematics, shows that the wave theory explanation
is simpler and better, and that the consequences are in
perfect agreement with observation. Indeed, quantita-
tive methods of reasoning enable us to deduce the ve-
locity of light in a refractive medium if we know how
the beam refracts when passing into it. Direct measure-
ments splendidly confirm these predictions, and thus
also the wave theory of light.

There still remains the question of color.

It must be remembered that a wave is characterized
by two numbers, its velocity and its wave-length. The
essential assumption of the wave theory of light is that

The Decline of the Mechanical View 117

different wave-lengths correspond to different colors.
The wave-length of homogeneous yellow light differs
from that of red or violet. Instead of the artificial
segregation of corpuscles belonging to various colors
we have the natural difference in wave-length.

It follows that Newton’s experiments on the disper-
sion of light can be described in two different lan-
guages, that of the corpuscular theory and that of the
wave theory. For example:

Corpuscular Language Wave Language
The corpuscles belonging The rays of different wave-
to different colors have the length belonging to differ-
same velocity in vacuo, but ent colors have the same
different velocities in glass, velocity in the ether, but

different velocities in glass.

White light is a composi- White light is a composi-
tion of corpuscles belong- tion of waves of all wave-
ing to different colors, lengths, whereas in the spec-
whereas in the spectrum trum they are separated,
they are separated.

It would seem wise to avoid the ambiguity resulting
from the existence of two distinct theories of the same
phenomena, by deciding in favor of one of them after
a careful consideration of the faults and merits of each.
The dialogue between N and H shows that this is no
easy task. The decision at this point would be more a
matter of taste than of scientific conviction. In New-
ton’s time, and for more than a hundred years after,
most physicists favored the corpuscular theory.

History brought in its verdict, in favor of the wave
theory of light and against the corpuscular theory, at

1 1 8 The Evolution of Physics

a much later date, the middle of the nineteenth cen-
tury. In his conversation with H, N stated that a de-
cision between the two theories was, in principle, ex-
perimentally possible. The corpuscular theory does not
allow light to bend, and demands the existence of sharp
shadows. According to the wave theory, on the other
hand, a sufficiently small obstacle will cast no shadow.
In the work of Young and Fresnel this result was ex-
perimentally realized and theoretical conclusions were
drawn.

An extremely simple experiment has already been
discussed, in which a screen with a hole was placed in
front of a point source of light and a shadow appeared
on the wall. We shall simplify the experiment further
by assuming that the source emits homogeneous light.
For the best results the source should be a strong one.
Let us imagine that the hole in the screen is made
smaller and smaller. If we use a strong source and
succeed in making the hole small enough, a new and
surprising phenomenon appears, something quite in-
comprehensible from the point of view of the corpus-
cular theory. There is no longer a sharp distinction
between light and dark. Light gradually fades into the
dark background in a series of light and dark rings.
The appearance of rings is very characteristic of a
wave theory. The explanation for alternating light and
dark areas will be clear in the case of a somewhat dif-
ferent experimental arrangement. Suppose we have a
sheet of dark paper with two pinholes through which
light may pass. If the holes are close together and very

PLATE II

( Photographed by V. Arkadiev)

Above, we see a photograph of light spots
after two beams have passed through two
pin holes, one after the other. (One pin hole
was opened, then covered and the other
opened.) Below, we see stripes when light
is allowed to pass through both pin holes
simultaneously.

Diffraction of light
bending around a
small obstacle.

by V. Arkadiev)

Diffraction of light
passing through a
smail hole.

The Decline of the Mechanical View 119

small, and if the source of homogeneous light is strong
enough, many light and dark bands will appear on the
wall, gradually fading off at the sides into the dark
background. The explanation is simple. A dark band is
where a trough of a wave from one pinhole meets the
crest of a wave from the other pinhole, so that the two
cancel. A band of light is where two troughs or two
crests from waves of the different pinholes meet and
reinforce each other. The explanation is more com-
plicated in the case of the dark and light rings of our
previous example in which we used a screen with one
hole, but the principle is the same. This appearance of
dark and light stripes in the case of two holes and of
light and dark rings in the case of one hole should be
borne in mind, for we shall later return to a discussion
of the two different pictures. The experiments de-
scribed here show the diffraction of light, the deviation
from the rectilinear propagation when small holes or
obstacles are placed in the way of the light wave.

With the aid of a little mathematics we are able to
go much further. It is possible to find out how great
or, rather, how small the wave-length must be to pro-
duce a particular pattern. Thus the experiments de-
scribed enable us to measure the wave-length of the
homogeneous light used as a source. To give an idea of
how small the numbers are we shall cite two wave-
lengths, those representing the extremes of the solar
spectrum, that is, the red and the violet.

The wave-length of red light is 0.00008 cm.

The wave-length of violet light is 0.00004 cm*

120 The Evolution of Physics

We should not be astonished that the numbers are so
small. The phenomenon of distinct shadow, that is, the
phenomenon of rectilinear propagation of light, is ob-
served in nature only because all apertures and ob-
stacles ordinarily met with are extremely large in com-
parison with the wave-lengths of light. It is only when
very small obstacles and apertures are used that light
reveals its wave-like nature.

But the story of the search for a theory of light is by
no means finished. The verdict of the nineteenth cen-
tury was not final and ultimate. For the modem physi-
cist the entire problem of deciding between corpuscles
and waves again exists, this time in a much more pro-
found and intricate form. Let us accept the defeat of
the corpuscular theory of light until we recognize the
problematic nature of the victory of the wave theory.

LONGITUDINAL OR TRANSVERSE LIGHT WAVES?

All the optical phenomena we have considered speak
for the wave theory. The bending of light around small
obstacles and the explanation of refraction are the
strongest arguments in its favor. Guided by the me-
chanical point of view we realize that there is still one
question to be answered: the determination of the me-
chanical properties of the ether. It is essential for the
solution of this problem to know whether light waves
in the ether are longitudinal or transverse. In other
words: is light propagated like sound? Is the wave due
to changes in the density of the medium, so that the
oscillations of the particles are in the direction of the

1 2 I

The Decline of the Mechanical View

propagation? Or does the ether resemble an elastic
jelly, a medium in which only transverse waves can be
set up and whose particles move in a direction per-
pendicular to that in which the wave itself travels?

Before solving this problem let us try to decide
which answer should be preferred. Obviously, we
should be fortunate if light waves were longitudinal.
The difficulties in designing a mechanical ether would
be much simpler in this case. Our picture of ether
might very probably be something like the mechanical
picture of a gas that explains the propagation of sound
waves. It would be much more difficult to form a pic-
ture of ether carrying transverse waves. To imagine a
jelly as a medium made up of particles in such a way
that transverse waves are propagated by means of it is
no easy task. Huygens believed that the ether would
turn out to be “air-like” rather than “jelly-like.” But
nature cares very little for our limitations. Was na-
ture, in this case, merciful to the physicists attempting
to understand all events from a mechanical point of
view? In order to answer this question we must discuss
some new experiments.

We shall consider in detail only one of many ex-
periments which are able to supply us with an answer.
Suppose we have a very thin plate of tourmaline
crystal, cut in a particular way which we need not de-
scribe here. The crystal plate must be thin so that we
are able to see a source of light through it. But now let
us take two such plates and place both of them be-
tween our eyes and the light. What do we expect to

122 The Evolution of Physics

see? Again a point of light, if the plates are sufficiently
thin. The chances are very good that the experiment
will confirm our expectation. Without worrying about
the statement that it may be chance, let us assume we
do see the light point through the two crystals. Now
let us gradually change the position of one of the
crystals by rotating it. This statement makes sense only
if the position of the axis about which the rotation
takes place is fixed. We shall take as an axis the line
determined by the incoming ray. This means that we
displace all the points of the one crystal except those

on the axis. A strange thing happens! The light gets
weaker and weaker until it vanishes completely. It re-
appears as the rotation continues and we regain the
initial view when the initial position is reached.

Without going into the details of this and similar

The Decline of the Mechanical View 123

experiments we can ask the following question: can
these phenomena be explained if the light waves are
longitudinal? In the case of longitudinal waves the par-
ticles of the ether would move along the axis, as the
beam does. If the crystal rotates, nothing along the axis
changes. The points on the axis do not move, and only
a very small displacement takes place nearby. No such
distinct change as the vanishing and appearance of a
new picture could possibly occur for a longitudinal
wave. This and many other similar phenomena can be
explained only by the assumption that light waves are
transverse and not longitudinal! Or, in other words,
the “jelly-like” character of the ether must be assumed.

This is very sad! We must be prepared to face tre-
mendous difficulties in the attempt to describe the
ether mechanically.

ETHER AND THE MECHANICAL VIEW

The discussion of all the various attempts to under-
stand the mechanical nature of the ether as a medium
for transmitting light, would make a long story. A me-
chanical construction means, as we know, that the sub-
stance is built up of particles with forces acting along
lines connecting them and depending only on the dis-
tance. In order to construct the ether as a jelly-like
mechanical substance physicists had to make some
highly artificial and unnatural assumptions. We shall
not quote them here; they belong to the almost for-
gotten past. But the result was significant and impor-
tant. The artificial character of all these assumptions,

124

The Evolution of Physics

the necessity for introducing so many of them all quite
independent of each other, was enough to shatter the
belief in the mechanical point of view.

But there are other and simpler objections to ether
than the difficulty of constructing it. Ether must be
assumed to exist everywhere, if we wish to explain op-
tical phenomena mechanically. There can be no empty
space if light travels only in a medium.

Yet we know from mechanics that interstellar space
does not resist the motion of material bodies. The
planets, for example, travel through the ether-jelly
without encountering any resistance such as a material
medium would offer to their motion. If ether does not
disturb matter in its motion, there can be no interac-
tion between particles of ether and particles of matter.
Light passes through ether and also through glass and
water, but its velocity is changed in the latter sub-
stances. How can this fact be explained mechanically?
Apparently only by assuming some interaction be-
tween ether particles and matter particles. We have
just seen that in the case of freely moving bodies such
interactions must be assumed not to exist. In other
words, there is interaction between ether and matter in
optical phenomena, but none in mechanical phenom-
ena! This is certainly a very paradoxical conclusion!

There seems to be only one way out of all these
difficulties. In the attempt to understand the phenom-
ena of nature from the mechanical point of view,
throughout the whole development of science up to the
twentieth century, it was necessary to introduce arti-

The Decline of the Mechanical View 125

ficial substances like electric and magnetic fluids, light
corpuscles, or ether. The result was merely the con-
centration of all the difficulties in a few essential points,
such as ether in the case of optical phenomena. Here
all the fruitless attempts to construct an ether in some
simple way, as well as the other objections, seem to
indicate that the fault lies in the fundamental assump-
tion that it is possible to explain all events in nature
from a mechanical point of view. Science did not suc-
ceed in carrying out the mechanical program con-
vincingly, and today no physicist believes in the pos-
sibility of its fulfillment.

In our short review of the principal physical ideas
we have met some unsolved problems, have come upon
difficulties and obstacles which discouraged the at-
tempts to formulate a uniform and consistent view of
all the phenomena of the external world. There was
the unnoticed clew in classical mechanics of the equal-
ity of gravitational and inertial mass. There was the
artificial character of the electric and magnetic fluids.
There was, in the interaction between electric current
and magnetic needle, an unsolved difficulty. It will be
remembered that this force did not act in the line con-
necting the wire and the magnetic pole, and depended
on the velocity of the moving charge. The law express-
ing its direction and magnitude was extremely compli-
cated. And finally, there was the great difficulty with
the ether.

Modem physics has attacked all these problems and
solved them. But in the struggle for these solutions

126

The Evolution of Physics

new and deeper problems have been created. Our
knowledge is now wider and more profound than that
of the physicist of the nineteenth century, but so are
our doubts and difficulties.

We Summarize:

In the old theories of electric fluids, in the corpuscular
and wave theories of light, we witness the further attempts
to apply the mechanical view. But in the realm of electric
and optical phenomena we meet grave difficulties in this
application.

A moving charge acts upon a magnetic needle. But the
force, instead of depending only upon distance, depends
also upon the velocity of the charge. The force neither
repels nor attracts but acts perpendicular to the line con-
necting the needle and the charge.

In optics we have to decide in favor of the wave theory
against the corpuscidar theory of light. Waves spreading
in a medium consisting of particles, with mechanical forces
acting between them, are certainly a mechanical concept.
But what is the medium through which light spreads and
what are its mechanical properties? There is no hope of
reducing the optical phenomena to the mechanical ones
before this question is answered. But the difficulties in
solving this problem are so great that we have to give it up
and thus give up the mechanical view as well.

III. FIELD, RELATIVITY

_____ J

Field, Relativity

The field, as representation . . . The two pillars of the field
theory .. .The reality of the field . . . Field and ether . . .
The mechanical scaffold .. .Ether and motion .. .Time,
distance , relativity . . . Relativity and mechanics ... The
time-space continuum . . . General relativity . . . Outside
and inside the elevator . . . Geometry and experiment . . .
General relativity and its verification . . . Field and matter

THE FIELD AS REPRESENTATION

During the second half of the nineteenth century new
and revolutionary ideas were introduced into physics;
they opened the way to a new philosophical view, dif-
fering from the mechanical one. The results of the
work of Faraday, Maxwell, and Hertz led to the devel-
opment of modern physics, to the creation of new con-
cepts, forming a new picture of reality.

Our task now is to describe the break brought about
in science by these new concepts and to show how
they gradually gained clarity and strength. We shall
try to reconstruct the line of progress logically, with-
out bothering too much about chronological order.

The new concepts originated in connection with the
phenomena of electricity, but it is simpler to introduce
them, for the first time, through mechanics. We know
that two particles attract each other and that this force
of attraction decreases with the square of the distance.

129

! 3 o

The Evolution of Physics

We can represent this fact in a new way, and shall do
so even though it is difficult to understand the advan-

tage of this. The small circle in our drawing represents
an attracting body, say, the sun. Actually, our diagram
should be imagined as a model in space and not as a
drawing on a plane. Our small circle, then, stands for a
sphere in space, say, the sun. A body, the so-called
test body , brought somewhere within the vicinity of
the sun will be attracted along the line connecting the
centers of the two bodies. Thus the lines in our draw-
ing indicate the direction of the attracting force of the
sun for different positions of the test body. The arrow
on each line shows that the force is directed toward
the sun; this means the force is an attraction. These are
the lines of force of the gravitational field. For the
moment, this is merely a name and there is no reason
for stressing it further. There is one characteristic fea-
ture of our drawing which will be emphasized later.

Field, Relativity 1 3 1

The lines of force are constructed in space, where no
matter is present. For the moment, all the lines of
force, or briefly speaking, the field , indicate only how
a test body would behave if brought into the vicinity
of the sphere for which the field is constructed.

The lines in our space model are always perpendicu-
lar to the surface of the sphere. Since they diverge
from one point, they are dense near the sphere and
become less and less so farther away. If we increase the
distance from the sphere twice or three times, then the
density of the lines, in our space-model, though not in
the drawing, will be four or nine times less. Thus the
lines serve a double purpose. On the one hand they
show the direction of the force acting on a body
brought into the neighborhood of the sphere-sun. On
the other hand the density of the lines of force in space
shows how the force varies with the distance. The
drawing of the field, correctly interpreted, represents
the direction of the gravitational force and its depend-
ence on distance. One can read the law of gravitation
from such a drawing just as well as from a description
of the action in words, or in the precise and econom-
ical language of mathematics. This field representation,
as we shall call it, may appear clear and interesting but
there is no reason to believe that it marks any real ad-
vance. It would be quite difficult to prove its usefulness
in the case of gravitation. Some may, perhaps, find it
helpful to regard these lines as something more than
drawings, and to imagine the real actions of force pass-
ing through them. This may be done, but then the

132 The Evolution of Physics

speed of the actions along the lines of force must be
assumed as infinitely great! The force between two
bodies, according to Newton’s law, depends only on
distance; time does not enter the picture. The force has
to pass from one body to another in no time! But, as
motion with infinite speed cannot mean much to any
reasonable person, an attempt to make our drawing
something more than a model leads nowhere.

We do not intend, however, to discuss the gravita-
tional problem just now. It served only as an introduc-
tion, simplifying the explanation of similar methods of
reasoning in the theory of electricity.

We shall begin with a discussion of the experiment
which created serious difficulties in our mechanical
interpretation. We had a current flowing through a
wire circuit in the form of a circle. In the middle of the
circuit was a magnetic needle. The moment the current
began to flow a new force appeared, acting on the
magnetic pole, and perpendicular to any line connect-
ing the wire and the pole. This force, if caused by a
circulating charge, depended, as shown by Rowland’s
experiment, on the velocity of the charge. These ex-
perimental facts contradicted the philosophical view
that all forces must act on the line connecting the par-
ticles and can depend only upon distance.

The exact expression for the force of a current act-
ing on a magnetic pole is quite complicated, much
more so, indeed, than the expression for gravitational
forces. We can, however, attempt to visualize the ac-
tions just as we did in the case of a gravitational force.

J 33

Field, Relativity

Our question is: with what force does the current act
upon a magnetic pole placed somewhere in its vicin-
ity? It would be rather difficult to describe this force
in words. Even a mathematical formula would be
complicated and awkward. It is best to represent all
we know about the acting forces by a drawing, or
rather by a spatial model, with lines of force. Some dif-
ficulty is caused by the fact that a magnetic pole exists
only in connection with another magnetic pole, form-
ing a dipole. We can, however, always imagine the
magnetic needle of such length that only the force act-
ing upon the pole nearer the current has to be taken
into account. The other pole is far enough away for
the force acting upon it to be negligible. To avoid am-
biguity we shall say that the magnetic pole brought
nearer to the wire is the positive one.

The character of the force acting upon the positive
magnetic pole can be read from our drawing.

First we notice an arrow near the wire indicating the
direction of the current, from higher to lower poten-

134 Tfeff Evolution of Physics

tial. All other lines are just lines of force belonging to
this current and lying on a certain plane. If drawn
properly, they tell us the direction of the force vector
representing the action of the current on a given posi-
tive magnetic pole as well as something about the
length of this vector. Force, as we know, is a vector
and to determine it we must know its direction as well
as its length. We are chiefly concerned with the prob-
lem of the direction of the force acting upon a pole.
Our question is: how can we find, from the drawing,
the direction of the force, at any point in space?

The rule for reading the direction of a force from
such a model is not as simple as in our previous exam-
ple, where the lines of force were straight. In our next
diagram only one line of force is drawn in order to

clarify the procedure. The force vector lies on the
tangent to the line of force, as indicated. The arrow of
the force vector and the arrows on the line of force
point in the same direction. Thus this is the direction
in which the force acts on a magnetic pole at this
point. A good drawing, or rather a good model, also

Field, Relativity 135

tells us something about the length of the force vector
at any point. This vector has to be longer where the
lines are denser, i.e., near the wire, shorter where the
lines are less dense, i.e., far from the wire.

In this way, the lines of force, or in other words, the
field, enable us to determine the forces acting on a
magnetic pole at any point in space. This, for the time
being, is the only justification for our elaborate con-
struction of the field. Knowing what the field ex-
presses, we shall examine with a far deeper interest the
lines of force corresponding to the current. These lines
are circles surrounding the wire and lying on the plane
perpendicular to that in which the wire is situated.
Reading the character of the force from the drawing
we come once more to the conclusion that the force
acts in a direction perpendicular to any line connecting
the wire and the pole, for the tangent to a circle is
always perpendicular to its radius. Our entire knowl-
edge of the acting forces can be summarized in the
construction of the field. We sandwich the concept of
the field between that of the current and that of the
magnetic pole in order to represent the acting forces
in a simple way.

Every current is associated with a magnetic field,
i.e., a force always acts on a magnetic pole brought
near the wire through which a current flows. We may
remark in passing that this property enables us to con-
struct sensitive apparatus for detecting the existence of
a current. Once having learned how to read the charac-

1 36 The Evolution of Physics

ter of the magnetic forces from the field model of a
current, we shall always draw the field surrounding
the wire through which the current flows, in order to
represent the action of the magnetic forces at any
point in space. Our first example is the so-called sole-
noid. This is, in fact, a coil of wire as shown in the
drawing. Our aim is to learn, by experiment, all we
can about the magnetic field associated with the cur-
rent flowing through a solenoid and to incorporate this
knowledge in the construction of a field. A drawing

represents our result. The curved fines of force are
closed, and surround the solenoid in a way character-
istic of the magnetic field of a current.

The field of a bar magnet can be represented in the
same way as that of a current. Another drawing shows
this. The fines of force are directed from the positive
to the negative pole. The force vector always lies on
the tangent to the fine of force and is longest near the
poles because the density of the fines is greatest at these
points. The force vector represents the action of the

137

Field, Relativity

magnet on a positive magnetic pole. In this case the
magnet and not the current is the “source” of the field.

Our last two drawings should be carefully com-
pared. In the first, we have the magnetic field of a cur-
rent flowing through a solenoid; in the second, the field
of a bar magnet. Let us ignore both the solenoid and
the bar and observe only the two outside fields. We
immediately notice that they are of exactly the same
character; in each case the fines of force lead from one
end of the solenoid or bar to the other.

The field representation yields its first fruit! It
would be rather difficult to see any strong similarity
between the current flowing through a solenoid and a
bar magnet if this were not revealed by our construc-
tion of the field.

The concept of field can now be put to a much
more severe test. We shall soon see whether it is any-
thing more than a new representation of the acting
forces. We could reason: assume, for a moment, that
the field characterizes all actions determined by its
sources in a unique way. This is only a guess. It would
mean that if a solenoid and a bar magnet have the same

138 The Evolution of Physics

field, then all their influences must also be the same. It
would mean that two solenoids, carrying electric cur-
rents, behave like two bar magnets, that they attract or
repel each other depending, exactly as in the case of
bars, on their relative positions. It would also mean that
a solenoid and a bar attract or repel each other in the
same way as two bars. Briefly speaking, it would mean
that all actions of a solenoid through which a current
flows, and of a corresponding bar magnet are the same,
since the field alone is responsible for them, and the
field in both cases is of the same character. Experiment
fully confirms our guess!

How difficult it would be to find those facts without
the concept of field! The expression for a force acting
between a wire through which a current flows and a
magnetic pole is very complicated. In the case of two
solenoids we should have to investigate the forces with
which two currents act upon each other. But if we do
this, with the help of the field, we immediately notice
the character of all those actions at the moment when
the similarity between the field of a solenoid and that
of a bar magnet is seen.

We have the right to regard the field as something
much more than we did at first. The properties of the
field alone appear to be essential for the description of
phenomena; the differences in source do not matter.
The concept of field reveals its importance by leading
to new experimental facts.

The field proved a very helpful concept. It began as
something placed between the source and the magnetic

*39

Field, Relativity

needle in order to describe the acting force. It was
thought of as an “agent” of the current, through which
all action of the current was performed. But now the
agent also acts as an interpreter, one who translates the
laws into a simple, clear language, easily understood.

The first success of the field description suggests
that it may be convenient to consider all actions of
currents, magnets and charges indirectly, i.e., with the
help of the field as an interpreter. A field may be re-
garded as something always associated with a current.
It is there even in the absence of a magnetic pole to test
its existence. Let us try to follow this new clew con-
sistently.

The field of a charged conductor can be introduced
in much the same way as the gravitational field, or the
field of a current or magnet. Again only the simplest
example! To design the field of a positively charged
sphere, we must ask what kind of forces are acting on

140 The Evolution of Physics

a small positively charged test body brought near the
source of the field, the charged sphere. The fact that
we use a positively and not a negatively charged test
body is merely a convention, indicating in which direc-
tion the arrows on the line of force should be drawn.
The model is analogous to that of a gravitational field
(p. 1 30) because of the similarity between Coulomb’s
law and Newton’s. The only difference between the
two models is that the arrows point in opposite direc-
tions. Indeed, we have repulsion of two positive
charges and attraction of two masses. However, the
field of a sphere with a negative charge will be iden-
tical with a gravitational field since the small positive
testing charge will be attracted by the source of the
field.

If both electric and magnetic poles are at rest, there
is no action between them, neither attraction nor re-
pulsion. Expressing the same fact in the field language

Field, Relativity 14;

we can say: an electrostatic field does not influence a
magnetostatic one and vice versa. The words “static
field” mean a field that does not change with time.
The magnets and charges would rest near one another
for an eternity if no external forces disturbed them.
Electrostatic, magnetostatic and gravitational fields are
all of different character. They do not mix; each pre-
serves its individuality regardless of the others.

Let us return to the electric sphere which was, until
now, at rest, and assume that it begins to move due to
the action of some external force. The charged sphere
moves. In the field language this sentence reads: the
field of the electric charge changes with time. But the
motion of this charged sphere is, as we already know
from Rowland’s experiment, equivalent to a current.
Further, every current is accompanied by a magnetic
field. Thus the chain of our argument is:

motion of charge -» change of an electric field
i

current -» associated magnetic field.

We, therefore, conclude: The change of an electric
field produced by the motion of a charge is always ac-
companied by a magnetic field.

Our conclusion is based on Oersted’s experiment but
it covers much more. It contains the recognition that
the association of an electric field, changing in time,
with a magnetic field is essential for our further argu-
ment.

As long as a charge is at rest there is only an electro-

14 2 The Evolution of Physics

static field. But a magnetic field appears as soon as the
charge begins to move. We can say more. The mag-
netic field created by the motion of the charge will be
stronger if the charge is greater and if it moves faster.
This also is a consequence of Rowland’s experiment.
Once again using the field language, we can say: the
faster the electric field changes, the stronger the ac-
companying magnetic field.

We have tried here to translate familiar facts from
the language of fluids, constructed according to the
old mechanical view, into the new language of fields.
We shall see later how clear, instructive, and far-
reaching our new language is.

THE TWO PILLARS OF THE FIELD THEORY

“The change of an electric field is accompanied by a
magnetic field.” If we interchange the words “mag-
netic” and “electric,” our sentence reads: “The change
of a magnetic field is accompanied by an electric field.”
Only an experiment can decide whether or not this
statement is true. But the idea of formulating this prob-
lem is suggested by the use of the field language.

Just over a hundred years ago, Faraday performed
an experiment which led to the great discovery of in-
duced currents.

The demonstration is very simple. We need only a
solenoid or some other circuit, a bar magnet, and one
of the many types of apparatus for detecting the exist-
ence of an electric current. To begin with, a bar mag-
net is kept at rest near a solenoid which forms a closed

H3

Field, Relativity

circuit. No current flows through the wire, for no
source is present. There is only the magnetostatic field
of the bar magnet which does not change with time.
Now, we quickly change the position of the magnet
either by removing it or by bringing it nearer the sole-
noid, whichever we prefer. At this moment, a current
will appear for a very short time and then vanish.

Whenever the position of the magnet is changed, the
current reappears, and can be detected by a sufficiently
sensitive apparatus. But a current— from the point of
view of the field theory— means the existence of an
electric field forcing the flow of the electric fluids
through the wire. The current, and therefore the elec-
tric field, too, vanishes when the magnet is again at
rest.

Imagine for a moment that the field language is un-
known and the results of this experiment have to be
described, qualitatively and quantitatively, in the lan-
guage of old mechanical concepts. Our experiment
then shows: by the motion of a magnetic dipole a new
force was created, moving the electric fluid in the wire.
The next question would be: upon what does this
force depend? This would be very difficult to answer.

144 The Evolution of Physics

We should have to investigate the dependence of the
force upon the velocity of the magnet, upon its shape,
and upon the shape of the circuit. Furthermore, this
experiment, if interpreted in the old language, gives us
no hint at all as to whether an induced current can be
excited by the motion of another circuit carrying a
current, instead of by motion of a bar magnet.

It is quite a different matter if we use the field lan-
guage and again trust our principle that the action is
determined by the field. We see at once that a solenoid
through which a current flows would serve as well as a
bar magnet. The drawing shows two solenoids: one,
small, through which a current flows, and the other,
in which the induced current is detected, larger. We

(raj

could move the small solenoid, as we previously moved
the bar magnet, creating an induced current in the
larger solenoid. Furthermore, instead of moving the
small solenoid, we could create and destroy a magnetic
field by creating and destroying the current, that is,
by opening and closing the circuit. Once again, new
facts suggested by the field theory are confirmed by
experiment!

Let us take a simpler example. We have a closed wire

145

Field, Relativity

without any source of current. Somewhere in the
vicinity is a magnetic field. It means nothing to us
whether the source of this magnetic field is another
circuit through which an electric current flows, or a

bar magnet. Our drawing shows the closed circuit and
the magnetic lines of force. The qualitative and quanti-
tative description of the induction phenomena is very
simple in terms of the field language. As marked on
the drawing, some lines of force go through the surface
bounded by the wire. We have to consider the lines of
force cutting that part of the plane which has the wire
for a rim. No electric current is present so long as the
field does not change, no matter how great its strength.
But a current begins to flow through the rim-wire as
soon as the number of lines passing through the surface
surrounded by wire changes. The current is deter-
mined by the change, however it may be caused, of the
number of lines passing the surface. This change in the
number of lines of force is the only essential concept

146 The Evolution of Physics

for both the qualitative and the quantitative descrip-
tions of the induced current. “The number of lines
changes” means that the density of the lines changes
and this, we remember, means that the field strength
changes.

These then are the essential points in our chain of
reasoning: change of magnetic field -» induced cur-
rent -> motion of charge -» existence of an electric
field.

Therefore: a changing magnetic field is accompanied
by an electric field.

Thus we have found the two most important pillars
of support for the theory of the electric and magnetic
field. The first is the connection between the changing
electric field and the magnetic field. It arose from
Oersted’s experiment on the deflection of a magnetic
needle and led to the conclusion: a changing electric
field is accompanied by a magnetic field.

The second connects the changing magnetic field
with the induced current and arose from Faraday’s
experiment. Both formed a basis for quantitative de-
scription.

Again the electric field accompanying the chang ing
magnetic field appears as something real. We had to
imagine, previously, the magnetic field of a current
existing without the testing pole. Similarly, we must
claim here that the electric field exists without the wire
testing the presence of an induced current.

In fact, our two-pillar structure could be reduced to
only one, namely, to that based on Oersted’s experi-

H7

Field, Relativity

ment. The result of Faraday’s experiment could be de-
duced from this with the law of conservation of en-
ergy. We used the two-pillar structure only for the
sake of clearness and economy.

One more consequence of the field description
should be mentioned. There is a circuit through which
a current flows, with for instance, a voltaic battery as
the source of the current. The connection between the
wire and the source of the current is suddenly broken.
There is, of course, no current now! But during this
short interruption an intricate process takes place, a
process which could again have been foreseen by the
field theory. Before the interruption of the current
there was a magnetic field surrounding the wire. This
ceased to exist the moment the current was inter-
rupted. Therefore, through the interruption of a cur-
rent, a magnetic field disappeared. The number of lines
of force passing through the surface surrounded by the
wire changed very rapidly. But such a rapid change,
however it is produced, must create an induced cur-
rent. What really matters is the change of the magnetic
field making the induced current stronger if the change
is greater. This consequence is another test for the
theory. The disconnection of a current must be accom-
panied by the appearance of a strong, momentary in-
duced current. Experiment again confirms the predic-
tion. Anyone who has ever disconnected a current
must have noticed that a spark appears. This spark re-
veals the strong potential differences caused by the
rapid change of the magnetic field.

148 The Evolution of Physics

The same process can be looked at from a different
point of view, that of energy. A magnetic field dis-
appeared and a spark was created. A spark represents
energy, therefore, so also must the magnetic field. To
use the field concept and its language consistently, we
must regard the magnetic field as a store of energy.
Only in this way shall we be able to describe the elec-
tric and magnetic phenomena in accordance with the
law of conservation of energy.

Starting as a helpful model the field became more
and more real. It helped us to understand old facts and
led us to new ones. The attribution of energy to the
field is one step further in the development in which
the field concept was stressed more and more, and the
concepts of substances, so essential to the mechanical
point of view, were more and more suppressed.

THE REALITY OF THE FIELD

The quantitative, mathematical description of the
laws of the field is summed up in what are called Max-
well’s equations. The facts mentioned so far led to the
formulation of these equations but their content is
much richer than we have been able to indicate. Their
simple form conceals a depth revealed only by careful
study.

The formulation of these equations is the most im-
portant event in physics since Newton’s time, not only
because of their wealth of content, but also because
they form a pattern for a new type of law.

The characteristic features of Maxwell’s equations,
appearing in all other equations of modern physics, are

Field, Relativity 149

summarized in one sentence. Maxwell’s equations are
laws representing the structure of the field.

Why do Maxwell’s equations differ in form and
character from the equations of classical mechanics?
What does it mean that these equations describe the
structure of the field? How is it possible that, from the
results of Oersted’s and Faraday’s experiments, we can
form a new type of law, which proves so important for
the further development of physics?

We have already seen, from Oersted’s experiment,
how a magnetic field coils itself around a changing
electric field. We have seen, from Faraday’s experi-
ment, how an electric field coils itself around a chang-
ing magnetic field. To outline some of the characteris-
tic features of Maxwell’s theory, let us, for the moment,
focus all our attention on one of these experiments,
say, on that of Faraday. We repeat the drawing in

which an electric current is induced by a changing mag-
netic field. We already know that an induced current

i5°

i

The Evolution of Physics

appears if the number of lines of force, passing the sur-
face bounded by the wire, changes. Then the current
will appear if the magnetic field changes or the circuit
is deformed or moved: if the number of magnetic lines
passing through the surface is changed, no matter how
this change is caused. To take into account all these
various possibilities, to discuss their particular influ-
ences, would necessarily lead to a very complicated
theory. But can we not simplify our problem? Let us
try to eliminate from our considerations everything
which refers to the shape of the circuit, to its length,
to the surface enclosed by the wire. Let us imagine
that the circuit in our last drawing becomes smaller and
smaller, shrinking gradually to a very small circuit en-
closing a certain point in space. Then everything con-
cerning shape and size is quite irrelevant. In this limit-
ing process where the closed curve shrinks to a point,
size and shape automatically vanish from our consid-
erations and we obtain laws connecting changes of
magnetic and electric field at an arbitrary point in
space at an arbitrary instant.

Thus, this is one of the principal steps leading to
Maxwell’s equations. It is again an idealized experiment
performed in imagination by repeating Faraday’s ex-
periment with a circuit shrinking to a point.

We should really call it half a step rather than a
whole one. So far our attention has been focused on
Faraday’s experiment. But the other pillar of the field
theory, based on Oersted’s experiment, must be consid-
ered just as carefully and in a similar manner. In this

Field, Relativity 1 5 1

experiment the magnetic lines of force coil themselves
around the current. By shrinking the circular magnetic
lines of force to a point, the second half-step is per-
formed and the whole step yields a connection be-
tween the changes of the magnetic and electric fields
at an arbitrary point in space and at an arbitrary instant.

But still another essential step is necessary. Accord-
ing to Faraday’s experiment, there must be a wire test-
ing the existence of the electric field, just as there must
be a magnetic pole, or needle, testing the existence of
a magnetic field in Oersted’s experiment. But Maxwell’s
new theoretical idea goes beyond these experimental
facts. The electric and magnetic field, or in short, the
electromagnetic field is, in Maxwell’s theory, some-
thing real. The electric field is produced by a changing
magnetic field, quite independently, whether or not
there is a wire to test its existence; a magnetic field is
produced by a changing electric field, whether or not
there is a magnetic pole to test its existence.

Thus two essential steps led to Maxwell’s equations.
The first: in considering Oersted’s and Rowland’s ex-
periments, the circular line of the magnetic field coil-
ing itself around the current and the changing electric
field, had to be shrunk to a point; in considering Fara-
day’s experiment, the circular line of the electric field
coiling itself around the changing magnetic field had to
be shrunk to a point. The second step consists of the
realization of the field as something real; the electro-
magnetic field once created exists, acts, and changes
according to Maxwell’s laws.

J 5 2

The Evolution of Physics

Maxwell’s equations describe the structure of the
electromagnetic field. All space is the scene of these
laws and not, as for mechanical laws, only points in
which matter or charges are present.

We remember how it was in mechanics. By knowing
the position and velocity of a particle at one single
instant, by knowing the acting forces, the whole future
path of the particle could be forseen. In Maxwell’s
theory, if we know the field at one instant only, we
can deduce from the equations of the theory how the
whole field will change in space and time. Maxwell’s
equations enable us to follow the history of the field,
just as the mechanical equations enabled us to follow
the history of material particles.

But there is still one essential difference between me-
chanical laws and Maxwell’s laws. A comparison of
Newton’s gravitational laws and Maxwell’s field laws
will emphasize some of the characteristic features ex-
pressed by these equations.

With the help of Newton’s laws we can deduce the
motion of the earth from the force acting between the
sun and the earth. The laws connect the motion of the
earth with the action of the far-off sun. The earth and-
the sun, though so far apart, are both actors in the play
of forces.

In Maxwell’s theory there are no material actors.
The mathematical equations of this theory express the
laws governing the electromagnetic field. They do not,
as in Newton’s laws, connect two widely separated
events; they do not connect the happenings here with

Field, Relativity 153

the conditions there. The field here and now depends
on the field in the immediate neighborhood at a time
fust past. The equations allow us to predict what will
happen a little further in space and a little later in time,
if we know what happens here and now. They allow
us to increase our knowledge of the field by small steps.
We can deduce what happens here from that which
happened far away by the summation of these very
small steps. In Newton’s theory, on the contrary, only
big steps connecting distant events are permissible. The
experiments of Oersted and Faraday can be regained
from Maxwell’s theory, but only by the summation of
small steps each of which is governed by Maxwell’s
equations.

A more thorough mathematical study of Maxwell’s
equations shows that new and really unexpected con-
clusions can be drawn and the whole theory submitted
to a test on a much higher level, because the theoretical
consequences are now of a quantitative character and
are revealed by a whole chain of logical arguments.

Let us again imagine an idealized experiment. A small
sphere with an electric charge is forced, by some ex-
ternal influence, to oscillate rapidly and in a rhythmical
way, like a pendulum. With the knowledge we already
have of the changes of the field, how shall we describe
everything that is going on here, in the field language?

The oscillation of the charge produces a changing
electric field. This is always accompanied by a chang-
ing magnetic field. If a wire forming a closed circuit is
placed in the vicinity, then again the changing mag-

154 The Evolution of Physics

netic field will be accompanied by an electric current
in the circuit. All this is merely a repetition of known
facts, but the study of Maxwell’s equations gives a
much deeper insight into the problem of the oscillating
electric charge. By mathematical deduction from Max-
well’s equations we can detect the character of the
field surrounding an oscillating charge, its structure
near and far from the source and its change with time.
The outcome of such deduction is the electromagnetic
wave. Energy radiates from the oscillating charge trav-
eling with a definite speed through space; but a trans-
ference of energy, the motion of a state, is character-
istic of all wave phenomena.

Different types of waves have already been consid-
ered. There was the longitudinal wave caused by the
pulsating sphere, where the changes of density were
propagated through the medium. There was the jelly-
like medium in which the transverse wave spread. A
deformation of the jelly, caused by the rotation of the
sphere, moved through the medium. What land of
changes are now spreading in the case of an electro-
magnetic wave? Just the changes of an electromagnetic
field! Every change of an electric field produces a mag-
netic field; every change of this magnetic field pro-
duces an electric field; every change of ... , and so
on. As field represents energy, all these changes spread-
ing out in space, with a definite velocity, produce a
wave. The electric and magnetic lines of force always
lie, as deduced from the theory, on planes perpendicu-
lar to the direction of propagation. The wave pro-

*55

Field, Relativity

duced is, therefore, transverse. The original features of
the picture of the field we formed from Oersted’s and
Faraday’s experiments are still preserved, but we now
recognize that it has a deeper meaning.

The electromagnetic wave spreads in empty space.
This, again, is a consequence of the theory. If the oscil-
lating charge suddenly ceases to move, then, its field
becomes electrostatic. But the series of waves created
by the oscillation continues to spread. The waves lead
an independent existence and the history of their
changes can be followed just as that of any other ma-
terial object.

We understand that our picture of an electromag-
netic wave, spreading with a certain velocity in space
and changing in time, follows from Maxwell’s equa-
tions only because they describe the structure of the
electromagnetic field at any point in space and for any
instant.

There is another very important question. With
what speed does the electromagnetic wave spread in
empty space? The theory, with the support of some
data from simple experiments having nothing to do
with the actual propagation of waves, gives a clear an-
swer: the velocity of cm electromagnetic wave is equal
to the velocity of light.

Oersted’s and Faraday’s experiments formed the
basis on which Maxwell’s laws were built. All our re-
sults so far have come from a careful study of these
laws, expressed in the field language. The theoretical
discovery of an electromagnetic wave spreading with

156 The Evolution of Physics

the speed of light is one of the greatest achievements in
the history of science.

Experiment has confirmed the prediction of theory.
Fifty years ago, Hertz proved, for the first time, the
existence of electromagnetic waves and confirmed ex-
perimentally that their velocity is equal to that of light.
Nowadays, millions of people demonstrate that elec-
tromagnetic waves are sent and received. Their ap-
paratus is far more complicated than that used by
Hertz and detects the presence of waves thousands of
miles from their sources instead of only a few yards.

FIELD AND ETHER

The electromagnetic wave is a transverse one and is
propagated with the velocity of light in empty space.
The fact that their velocities are the same suggests a
close relationship between optical and electromagnetic
phenomena.

When we had to choose between the corpuscular
and the wave theory, we decided in favor of the wave
theory. The diffraction of light was the strongest ar-
gument influencing our decision. But we shall not con-
tradict any of the explanations of the optical facts by
also assuming that the light wave is an electromagnetic
one. On the contrary, still other conclusions can be
drawn. If this is really so, then there must exist some
connection between the optical and electrical proper-
ties of matter that can be deduced from the theory.
The fact that conclusions of this kind can really be
drawn and that they stand the test of experiment is an

Field, Relativity 157

essential argument in favor of the electromagnetic the-
ory of light.

This great result is due to the field theory. Two ap-
parently unrelated branches of science are covered by
the same theory. The same Maxwell’s equations de-
scribe both electric induction and optical refraction. If
it is our aim to describe everything that ever happened
or may happen with the help of one theory, then the
union of optics and electricity is, undoubtedly, a very
great step forward. From the physical point of view,
the only difference between an ordinary electromag-
netic wave and a light wave is the wave-length: this is
very small for light waves, detected by the human eye,
and great for ordinary electromagnetic waves, detected
by a radio receiver.

The old mechanical view attempted to reduce all
events in nature to forces acting between material par-
ticles. Upon this mechanical view was based the first
naive theory of the electric fluids. The field did not
exist for the physicist of the early years of the nine-
teenth century. For him only substance and its changes
were real. He tried to describe the action of two elec-
tric charges only by concepts referring directly to the
two charges.

In the beginning, the field concept was no more than
a means of facilitating the understanding of phenomena
from the mechanical point of view. In the new field
language it is the description of the field between the
two charges, and not the charges themselves, which is
essential for an understanding of their action. The rec-

x 58 The Evolution of Physics

ognition of the new concepts grew steadily, until sub-
stance was overshadowed by the field. It was realized
that something of great importance had happened in
physics. A new reality was created, a new concept for
which there was no place in the mechanical descrip-
tion. Slowly and by a struggle the field concept es-
tablished for itself a leading place in physics and has
remained one of the basic physical concepts. The elec-
tromagnetic field is, for the modem physicist, as real
as the chair on which he sits.

But it would be unjust to consider that the new field
view freed science from the errors of the old theory of
electric fluids or that the new theory destroys the
achievements of the old. The new theory shows the
merits as well as the limitations of the old theory and
allows us to regain our old concepts from a higher
level. This is true not only for the theories of electric
fluids and field, but for all changes in physical theories,
however revolutionary they may seem. In our case, we
still find, for example, the concept of the electric
charge in Maxwell’s theory, though the charge is un-
derstood only as a source of the electric field. Cou-
lomb s law is still valid and is contained in Maxwell’s
equations from which it can be deduced as one of the
many consequences. We can still apply the old theory,
whenever facts within the region of its validity are in-
vestigated. But we may as well apply the new theory,
since all the known facts are contained in the realm of
its validity.

To use a comparison, we could say that creating a

159

Field, Relativity

new theory is not like destroying an old barn and erect-
ing a skyscraper in its place. It is rather like climbing a
mountain, gaining new and wider views, discovering
unexpected connections between our starting point and
its rich environment. But the point from which we
started out still exists and can be seen, although it ap-
pears smaller and forms a tiny part of our broad view
gained by the mastery of the obstacles on our adven-
turous way up.

It was, indeed, a long time before the full content of
Maxwell’s theory was recognized. The field was at first
considered as something which might later be inter-
preted mechanically with the help of ether. By the
time it was realized that this program could not be car-
ried out, the achievements of the field theory had al-
ready become too striking and important for it to be
exchanged for a mechanical dogma. On the other hand,
the problem of devising the mechanical model of ether
seemed to become less and less interesting and the re-
sult, in view of the forced and artificial character of
the assumptions, more and more discouraging.

Our only way out seems to be to take for granted
the fact that space has the physical property of trans-
mitting electromagnetic waves, and not to bother too
much about the meaning of this statement. We may
still use the word ether, but only to express some phys-
ical property of space. This word ether has changed its
meaning many times in the development of science. At
the moment it no longer stands for a medium built up

i6o The Evolution of Physics

of particles. Its story, by no means finished, is con-
tinued by the relativity theory.

THE MECHANICAL SCAFFOLD

On reaching this stage of our story we must turn
back to the beginning, to Galileo’s law of inertia. We
quote once more:

Every body perseveres in its state of rest, or of uniform
motion in a right line, unless it is compelled to change that
state by forces impressed thereon.

Once the idea of inertia is understood, one wonders
what more can be said about it. Although this problem
has already been thoroughly discussed, it is by no
means exhausted.

Imagine a serious scientist who believes that the law
of inertia can be proved or disproved by actual experi-
ments. He pushes small spheres along a horizontal
table, trying to eliminate friction so far as possible. He
notices that the motion becomes more uniform as the
table and the spheres are made smoother. Just as he is
about to proclaim the principle of inertia, someone
suddenly plays a practical joke on him. Our physicist
works in a room without windows and has no com-
munication whatever with the outside world. The
practical joker installs some mechanism which enables
him to cause the entire room to rotate quickly on an
axis passing through its center. As soon as the rotation
begins, the physicist has new and unexpected experi-
ences. The sphere which has been moving uniformly

Field, Relativity 1 6 1

tries to get as far away from the center and as near to
the walls of the room as possible. He himself feels a
strange force pushing him against the wall. He experi-
ences the same sensation as anyone in a train or car
traveling fast around a curve, or even more, on a rotat-
ing merry-go-round. All his previous results go to
pieces.

Our physicist would have to discard, with the law
of inertia, all mechanical laws. The law of inertia was
his starting point; if this is changed so are all his fur-
ther conclusions. An observer destined to spend his
whole life in the rotating room and to perform all his
experiments there, would have laws of mechanics dif-
fering from ours. If, on the other hand, he enters the
room with a profound knowledge and a firm belief in
the principles of physics, his explanation for the ap-
parent breakdown of mechanics would be the assump-
tion that the room rotates. By mechanical experiments
he could even ascertain how it rotates.

Why should we take so much interest in the ob-
server in his rotating room? Simply because we, on
our earth, are to a certain extent, in the same position.
Since the time of Copernicus we have known that the
earth rotates on its axis and moves around the sun. Even
this simple idea, so clear to everyone, was not left
untouched by the advance of science. But let us leave
this question for the time being and accept Copernicus’
point of view. If our rotating observer could not con-
firm the laws of mechanics we, on our earth, should
also be unable to do so. But the rotation of the earth is

1 62 The Evolution of Physics

comparatively slow, so that the effect is not very dis-
tinct. Nevertheless there are many experiments which
show a small deviation from the mechanical laws, and
their consistency can be regarded as proof of the rota-
tion of the earth.

Unfortunately we cannot place ourselves between
the sun and the earth, to prove there the exact validity
of the law of inertia and to get a view of the rotating
earth. This can be done only in imagination. All our
experiments must be performed on the earth on which
we are compelled to live. The same fact is often ex-
pressed more scientifically: the earth is our co-ordinate
system.

To show the meaning of these words more clearly,
let us take a simple example. We can predict the posi-
tion, at any time, of a stone thrown from a tower, and
confirm our prediction by observation. If a measuring-
rod is placed beside the tower, we can foretell with
what point of the rod the falling body will coincide at
any given moment. The tower and scale must, obvi-
ously, not be made of rubber or any other material
which would undergo any change during the experi-
ment. In fact, the unchangeable scale, rigidly con-
nected with the earth, and a good clock are all we
need, in principle, for the experiment. If we have these,
we can ignore not only the architecture of the tower,
but its very presence. The foregoing assumptions are
all trivial and not usually specified in descriptions of
such experiments. But this analysis shows how many
hidden assumptions there are in every one of our state-

Field, Relativity 163

ments. In our case, we assumed the existence of a rigid
bar and an ideal clock, without which it would be im-
possible to check Galileo’s law for falling bodies. With
this simple but fundamental physical apparatus, a rod
and a clock, we can confirm this mechanical law with
a certain degree of accuracy. Carefully performed, this
experiment reveals discrepancies between theory and
experiment due to the rotation of the earth or, in other
words, to the fact that the laws of mechanics, as here
formulated, are not strictly valid in a co-ordinate sys-
tem rigidly connected with the earth.

In all mechanical experiments, no matter of what
type, we have to determine positions of material points
at some definite time, just as in the above experiment
with a falling body. But the position must always be
described with respect to something, as in the previous
case to the tower and the scale. We must have what we
call some frame of reference, a mechanical scaffold, to
be able to determine the positions of bodies. In describ-
ing the positions of objects and men in a city, the
streets and avenues form the frame to which we refer.
So far we have not bothered to describe the frame
when quoting the laws of mechanics, because we hap-
pen to live on the earth and there is no difficulty in any
particular case in fixing a frame of reference, rigidly
connected with the earth. This frame, to which we
refer all our observations, constructed of rigid un-
changeable bodies, is called the co-ordinate system.
Since this expression will be used very often, we shall
simply write CS.

164 The Evolution of Physics

All our physical statements thus far have lacked
something. We took no notice of the fact that all ob-
servations must be made in a certain CS. Instead of
describing the structure of this CS we just ignored its
existence. For example, when we wrote “a body moves
uniformly . . .” we should really have written, “A
body moves uniformly, relative to a chosen CS. . . .”
Our experience with the rotating room taught us that
the results of mechanical experiments may depend on
the CS chosen.

If two CS rotate with respect to each other, then the
laws of mechanics cannot be valid in both. If the sur-
face of the water in a swimming pool, forming one of
the co-ordinate systems, is horizontal, then in the other
the surface of the water in a similar swimming pool
takes the curved form familiar to anyone who stirs his
coffee with a spoon.

When formulating the principal clews of mechanics
we omitted one important point. We did not state for
which CS they are valid. For this reason, the whole of
classical mechanics hangs in mid-air since we do not
know to which frame it refers. Let us, however, pass
over this difficulty for the moment. We shall make the
slightly incorrect assumption that in every CS rigidly
connected with the earth, the laws of classical me-
chanics are valid. This is done in order to fix the CS
and to make our statements definite. Although our
statement that the earth is a suitable frame of reference
is not wholly correct, we shall accept it for the present.

We assume, therefore, the existence of one CS for

Field, Relativity 165

which the laws of mechanics are valid. Is this the only
one? Suppose we have a CS such as a train, a ship or
an airplane moving relative to our earth. Will the
laws of mechanics be valid for these new CS? We
know definitely that they are not always valid as for
instance in the case of a train turning a curve, a ship
tossed in a storm, or an airplane in a tail spin. Let us
begin with a simple example. A CS moves uniformly,
relative to our “good” CS, that is, one in which the
laws of mechanics are valid. For instance, an ideal
train or a ship sailing with delightful smoothness along
a straight line and with a never-changing speed. We
know from everyday experience that both systems will
be “good,” that physical experiments performed in a
uniformly moving train or ship will give exactly the
same results as on the earth. But, if the train stops, or
accelerates abruptly, or if the sea is rough, strange
things happen. In the train, the trunks fall off the lug-
gage racks, on the ship tables and chairs are thrown
about and the passengers become seasick. From the
physical point of view this simply means that the laws
of mechanics cannot be applied to these CS, that they
are “bad” CS.

This result can be expressed by the so-called Galilean
relativity principle : if the laws of mechanics are valid
in one CS, then they are valid in any other CS moving
uniformly relative to the first.

If we have two CS moving non-uniformly, rela-
tive to each other, then the laws of mechanics can-
not be valid in both. “Good” co-ordinate systems, that

1 66 The Evolution of Physics

is, those for which the laws of mechanics are valid, we
call inertial systems. The question as to whether an
inertial system exists at all is still unsettled. But if there
is one such system, then there is an infinite number of
them. Every CS moving uniformly, relative to the
initial one, is also an inertial CS.

Let us consider the case of two CS starting from a
known position and moving uniformly, one relative
to the other, with a known velocity. One who prefers
concrete pictures can safely think of a ship or a tr ain
moving relative to the earth. The laws of mechanics
can be confirmed experimentally with the same degree
of accuracy, on the earth or in a train or on a ship mov-
ing uniformly. But some difficulty arises if the observ-
ers of two systems begin to discuss observations of the
same event from the point of view of their different
CS. Each would like to translate the other’s observa-
tions into his own language. Again a simple example:
the same motion of a particle is observed from two CS,
the earth and a train moving uniformly. These are
both inertial. Is it sufficient to know what is observed
in one CS in order to find out what is observed in the
other, if the relative velocities and positions of the two
CS at some moment are known? It is most essential, for
a description of events, to know how to pass from one
CS to another, since both CS are equivalent and both
equally suited for the description of events in nature.
Indeed, it is quite enough to know the results obtained
by an observer in one CS to know those obtained by an
observer in the other.

Field, Relativity 167

Let us consider the problem more abstractly, with-
out ship or train. To simplify matters we shall investi-
gate only motion along straight lines. We have, then,
a rigid bar with a scale and a good clock. The rigid
bar represents, in the simple case of rectilinear motion,
a CS just as did the scale on the tower in Galileo’s ex-
periment. It is always simpler and better to think of a
CS as a rigid bar in the case of rectilinear motion and
a rigid scaffold built of parallel and perpendicular rods
in the case of arbitrary motion in space, disregarding
towers, walls, streets, and the like. Suppose we have, in
our simplest case, two CS, that is two rigid rods; we
draw one above the other and call them respectively
the “upper” and “lower” CS. We assume that the two
CS move with a definite velocity relative to each
other, so that one slides along the other. It is safe to
assume that both rods are of infinite length and have
initial points but no end points. One clock is sufficient
for the two CS, for the time flow is the same for both.
When we begin our observation the starting points of
the two rods coincide. The position of a material point
is characterized, at this moment, by the same number in
both CS. The material point coincides with a point on
the scale on the rod, thus giving us a number determin-
ing the position of this material point. But, if the rods
move uniformly, relative to each other, the numbers
corresponding to the positions will be different after
some time, say, one second. Consider a material point
resting on the upper rod. The number determining its
position on the upper CS does not change with time.

168 The Evolution of Physics

But the corresponding number for the lower rod will
change. Instead of “the number corresponding to a
position of the point,” we shall say briefly, the co-

<

< >

ordinate of a point. Thus we see from our drawing that
although the following sentence sounds intricate, it is
nevertheless correct and expresses something very sim-
ple. The co-ordinate of a point in the lower CS is equal
to its co-ordinate in the upper CS plus the co-ordinate
of the origin of the upper CS relative to the lower CS.
The important thing is that we can always calculate
the position of a particle in one CS if we know the
position in the other. For this purpose we have to
know the relative positions of the two co-ordinate sys-
tems in question at every moment. Although all this
sounds learned it is, really, very simple and hardly
worth such detailed discussion, except that we shall
find it useful later.

It is worth our while to notice the difference be-
tween determining the position of a point and the time
of an event. Every observer has his own rod which
forms his CS, but there is only one clock for them all.
Time is something “absolute” which flows in the same
way for all observers in all CS.

Now another example. A man strolls with a velocity
of three miles per hour along the deck of a large ship.

Field, Relativity 169

This is his velocity relative to the ship, or, in other
words, relative to a CS rigidly connected with the ship.
If the velocity of the ship is thirty miles per hour rela-
tive to the shore, and if the uniform velocities of man
and ship both have the same direction, then the ve-
locity of the stroller will be thirty-three miles per hour
relative to an observer on the shore, or three miles per
hour relative to the ship. We can formulate this fact
more abstractly: the velocity of a moving material
point, relative to the lower CS, is equal to that relative
to the upper CS plus or minus the velocity of the upper
CS relative to the lower, depending upon whether the
velocities have the same or opposite directions. We
can, therefore, always transform not only positions,

>

but also velocities, from one CS to another if we know
the relative velocities of the two CS. The positions, or
co-ordinates, and velocities are examples of quantities
which are different in different CS bound together by
certain, in this case very simple, transformation laws.

There exist quantities, however, which are the same
in both CS and for which no transformation laws are
needed. Take as an example not one, but two fixed
points on the upper rod and consider the distance be-
tween them. This distance is the difference in the co-
ordinates of the two points. To find the positions of

i7° The Evolution of Physics

two points relative to different CS, we have to use
transformation laws. But in constructing the differ-

j < — -- > j

■*. >

ences of two positions the contributions due to the
different CS cancel each other and disappear, as is evi-
dent from the drawing. We have to add and subtract
' the distance between the origins of two CS. The dis-
tance of two points is, therefore, invariant , that is, in-
dependent of the choice of the CS.

The next example of a quantity independent of the
CS is the change of velocity, a concept familiar to us
from mechanics. Again, a material point moving along
a straight line is observed from two CS. Its change of
velocity is, for the observer in each CS, a difference
between two velocities, and the contribution due to
the uniform relative motion of the two CS disappears
when the difference is calculated. Therefore, the
change of velocity is an invariant, though only, of
course, on condition that the relative motion of our
two CS is uniform. Otherwise, the change of velocity
would be different in each of the two CS, the differ-
ence being brought in by the change of velocity of the
relative motion of the two rods, representing our co-
ordinate systems.

Now the last example! We have two material points,
with forces acting between them which depend only

Field, Relativity 1 7 1

on the distance. In the case of rectilinear motion, the
distance, and therefore the force as well, is invariant.
Newton’s law connecting the force with the change of
velocity will, therefore, be valid in both CS. Once
again we reach a conclusion which is confirmed by
everyday experience: if the laws of mechanics are valid
in one CS, then they are valid in all CS moving uni-
formly with respect to that one. Our example was, of
course, a very simple one, that of rectilinear motion in
which the CS can be represented by a rigid rod. But
our conclusions are generally valid, and can be sum-
marized as follows:

1. We know of no rule for finding an inertial system.
Given one, however, we can find an infinite num-
ber, since all CS moving uniformly, relative to each
other, are inertial systems if one of them is.

2. The time corresponding to an event is the same in
all CS. But the co-ordinates and velocities are dif-
ferent, and change according to the transformation
laws.

3. Although the co-ordinates and velocity change
when passing from one CS to another, the force
and change of velocity, and therefore the laws of
mechanics are invariant with respect to the trans-
formation laws.

The laws of transformation formulated here for co-
ordinates and velocities we shall call the transforma-
tion laws of classical mechanics, or more briefly, the
classical transformation.

The Evolution of Thy sics

172

ETHER AND MOTION

The Galilean relativity principle is valid for me-
chanical phenomena. The same laws of mechanics
apply to all inertial systems moving relative to each
other. Is this principle also valid for nonmechanical
phenomena, especially for those for which the field
concepts proved so very important? All problems con-
centrated around this question immediately bring us to
the starting point of the relativity theory.

We remember that the velocity of light in vacuo , or
in other words, in ether, is 186,000 miles per second
and that light is an electromagnetic wave spreading
through the ether. The electromagnetic field carries
energy which, once emitted from its source, leads an
independent existence. For the time being, we shall
continue to believe that the ether is a medium through
which electromagnetic waves, and thus also light
waves, are propagated, even though we are fully aware
of the many difficulties connected with its mechanical
structure.

We are sitting in a closed room so isolated from the
external world that no air can enter or escape. If we sit
still and talk we are, from the physical point of view,
creating sound waves, which spread from their resting
source with the velocity of sound in air. If there were
no air or other material medium between the mouth
and the ear, we could not detect a sound. Experiment
has shown that the velocity of sound in air is the same

Field, Relativity 173

in all directions, if there is no wind and the air is at
rest in the chosen CS.

Let us now imagine that our room moves uniformly
through space. A man outside sees, through the glass
walls of the moving room (or train if you prefer)
everything which is going on inside. From the meas-
urements of the inside observer he can deduce the ve-
locity of sound relative to his CS connected with his
surroundings, relative to which the room moves. Here
again is the old, much discussed, problem of determin-
ing the velocity in one CS if it is already known in
another.

The observer in the room claims: the velocity of
sound is, for me, the same in all directions.

The outside observer claims: the velocity of sound,
spreading in the moving room and determined in my
CS, is not the same in all directions. It is greater than
the standard velocity of sound in the direction of the
motion of the room and smaller in the opposite direc-
tion.

These conclusions are drawn from the classical trans-
formation and can be confirmed by experiment. The
room carries within it the material medium, the air
through which sound waves are propagated, and the
velocities of sound will, therefore, be different for the
inside and outside observer.

We can draw some further conclusions from the
theory of sound as a wave propagated through a ma-
terial medium. One way, though by no means the
simplest, of not hearing what someone is saying, is to

r 74 The Evolution of Physics

run, with a velocity greater than that of sound, rela-
tive to the air surrounding the speaker. The sound
waves produced will then never be able to reach our
ears. On the other hand, if we missed an important
word which will never be repeated, we must run with
a speed greater than that of sound to reach the pro-
duced wave and to catch the word. There is nothing
irrational in either of these examples except that in
both cases we should have to run with a speed of about
four hundred yards per second, and we can very well
imagine that further technical development will make
such speeds possible. A bullet fired from a gun actually
moves with a speed greater than that of sound and a
man placed on such a bullet would never hear the
sound of the shot.

All these examples are of a purely mechanical char-
acter and we can now formulate the important ques-
tions: could we repeat what has just been said of a
sound wave, in the case of a light wave? Do the Gali-
lean relativity principle and the classical transforma-
tion apply to mechanical as well as to optical and elec-
trical phenomena? It would be risky to answer these
questions by a simple “yes” or “no” without going
more deeply into their meaning.

In the case of the sound wave in the room moving
uniformly, relative to the outside observer, the follow-
ing intermediate steps are very essential for our con-
clusion:

The moving room carries the air in which the sound
wave is propagated.

i75

Field, Relativity

The velocities observed in two CS moving uniformly,
relative to each other, are connected by the classical
transformation.

The corresponding problem for light must be for-
mulated a little differently. The observers in the room
are no longer talking, but are sending light signals, or
light waves in every direction. Let us further assume
that the sources emitting the light signals are perma-
nently resting in the room. The light waves move
through the ether just as the sound waves moved
through the air.

Is the ether carried with the room as the air was?
Since we have no mechanical picture of the ether it is
extremely difficult to answer this question. If the room
is closed, the air inside is forced to move with it. There
is obviously no sense in thinking of ether in this way,
since all matter is immersed in it and it penetrates
everywhere. No doors are closed to ether. The “mov-
ing room,” now means only a moving CS to which the
source of light is rigidly connected. It is, however, not
beyond us to imagine that the room moving with its
light source carries the ether along with it just as the
sound source and air were carried along in the closed
room. But we can equally well imagine the opposite:
that the room travels through the ether as a ship
through a perfectly smooth sea, not carrying any part
of the medium along but moving through it. In our
first picture, the room moving with its light source
carries the ether. An analogy with a sound wave is pos-
sible and quite similar conclusions can be drawn. In the

176 The Evolution of Physics

second, the room moving with its light source does not
carry the ether. No analogy with a sound wave is pos-
sible and the conclusions drawn in the case of a sound
wave do not hold for a light wave. These are the two
limiting possibilities. We could imagine the still more
complicated possibility that the ether is only partially
carried by the room moving with its light source. But
there is no reason to discuss the more complicated as-
sumptions before finding out which of the two simpler
limiting cases experiment favors.

We shall begin with our first picture and assume, for
the present: the ether is carried along by the room
moving with its rigidly-connected light source. If we
believe in the simple transformation principle for the
velocities of sound waves, we can now apply our con-
clusions to light waves as well. There is no reason for
doubting the simple mechanical transformation law
which only states that the velocities have to be added
in certain cases and subtracted in others. For the mo-
ment, therefore, we shall assume both the carrying of
the ether by the room moving with its light source and
the classical transformation.

If I turn on the light and its source is rigidly con-
nected with my room, then the velocity of the light
signal has the well-known experimental value 186,000
miles per second. But the outside observer will notice
the motion of the room, and, therefore, that of the
source and, since the ether is carried along, his con-
clusion must be: the velocity of light in my outside CS
is different in different directions. It is greater than the

Field, Relativity 177

standard velocity of light in the direction of the mo-
tion of the room and smaller in the opposite direction.
Our conclusion is: if ether is carried with the room
moving with its light source and if the mechanical laws
are valid, then the velocity of light must depend on the
velocity of the light source. Light reaching our eyes
from a moving light source would have a greater ve-
locity if the motion is toward us and smaller if it is
away from us.

If our speed were greater than that of light we
should be able to run away from a light signal. We
could see occurrences from the past by reaching pre-
viously sent light waves. We should catch them in a
reverse order to that in which they were sent, and the
train of happenings on our earth would appear like a
film shown backward, beginning with a happy end-
ing. These conclusions all follow from the assump-
tion that the moving CS carries along the ether and the
mechanical transformation laws are valid. If this is so,
the analogy between light and sound is perfect.

But there is no indication as to the truth of these
conclusions. On the contrary, they are contradicted by
all observations made with the intention of proving
them. There is not the slightest doubt as to the clarity
of this verdict, although it is obtained through rather
indirect experiments in view of the great technical diffi-
culties caused by the enormous value of the velocity of
light. The velocity of light is always the same in all CS
independent of whether or not the emitting source
moves, or how it moves.

178 The Evolution of Physics

We shall not go into detailed description of the
many experiments from which this important conclu-
sion can be drawn. We can, however, use some very
simple arguments which, though they do not prove
that the velocity of light is independent of the motion
of the source, nevertheless make this fact convincing
and understandable.

In our planetary system the earth and other planets
move around the sun. We do not know of the existence
of other planetary systems, similar to ours. There are,
however, very many double-star systems, consisting of
two stars moving around a point, called their center of
gravity. Observation of the motion of these double
stars reveals the validity of Newton’s gravitational law.
Now suppose that the speed of light depends on the
velocity of the emitting body. Then the message, that
is, the light ray from the star, will travel more quickly
or more slowly, according to the velocity of the star at
the moment the ray is emitted. In this case the whole
motion would be muddled and it would be impossible
to confirm, in the case of distant double stars, the
validity of the same gravitational law which rules over
our planetary system.

Let us consider another experiment based upon a
very simple idea. Imagine a wheel rotating very
quickly. According to our assumption, the ether is car-
ried by the motion and takes a part in it. A light wave
passing near the wheel would have a different speed
when the wheel is at rest than when it is in motion.
The velocity of light in ether at rest should differ from

Field, Relativity 1 79

that in ether which is being quickly dragged round by
the motion of the wheel, just as the velocity of a sound
wave varies on calm and windy days. But no such
difference is detected! No matter from which angle
we approach the subject, or what crucial experiment
we may devise, the verdict is always against the as-
sumption of the ether carried by motion. Thus, the
result of our considerations, supported by more de-
tailed and technical argument, is:

The velocity of light does not depend on the motion
of the emitting source.

It must not be assumed that the moving body carries
the surrounding ether along.

We must, therefore, give up the analogy between
sound and light waves and turn to the second possibil-
ity: that all matter moves through the ether, which
takes no part whatever in the morion. This means that
we assume the existence of a sea of ether with all CS
resting in it, or moving relative to it. Suppose we
leave, for a while, the question as to whether experi-
ment proved or disproved this theory. It will be better
to become more familiar with the meaning of this new
assumption and with the conclusions which can be
drawn from it.

There exists a CS resting relative to the ether-sea.
In mechanics, not one of the many CS moving uni-
formly, relative to each other, could be distinguished.
All such CS were equally “good” or “bad.” If we have
two CS moving uniformly, relative to each other, it is
meaningless, in mechanics, to ask which of them is in

180 The Evolution of Physics

motion and which at rest. Only relative uniform mo-
tion can be observed. We cannot talk about absolute
uniform motion because of the Galilean relativity
principle. What is meant by the statement that absolute
and not only relative uniform motion exists? Simply
that there exists one CS in which some of the laws of
nature are different from those in all others. Also that
every observer can detect whether his CS is at rest or
in motion by comparing the laws valid in it with those
valid in the only one which has the absolute monopoly
of serving as the standard CS. Here is a different state
of affairs from classical mechanics, where absolute
uniform motion is quite meaningless because of Gali-
leo’s law of inertia.

What conclusions can be drawn in the domain of
field phenomena if motion through ether is assumed?
This would mean that there exists one CS distinct from
all others, at rest relative to the ether-sea. It is quite
clear that some of the laws of nature must be different
in this CS, otherwise the phrase, “motion through
ether,” would be meaningless. If the Galilean relativity
principle is valid then motion through ether makes no
sense at all. It is impossible to reconcile these two ideas.
If, however, there exists one special CS fixed by the
ether, then to speak of “absolute motion” or “absolute
rest,” has a definite meaning.

We really have no choice. We tried to save the
Galilean relativity principle by assuming that systems
carry the ether along in their motion, but this led to a
contradiction with experiment. The only way out is to

Field, Relativity 181

abandon the Galilean relativity principle and try out
the assumption that all bodies move through the calm
ether-sea.

The next step is to consider some conclusions con-
tradicting the Galilean relativity principle and sup-
porting the view of motion through ether, and to put
them to the test of an experiment. Such experiments
are easy enough to imagine, but very difficult to per-
form. As we are concerned here only with ideas, we
need not bother with technical difficulties.

Again we return to our moving room with two ob-
servers, one inside and one outside. The outside ob-
server will represent the standard CS, designated by
the ether-sea. It is the distinguished CS in which the
velocity of light always has the same standard value.
All fight sources, whether moving or at rest in the
calm ether-sea, propagate fight with the same velocity.
The room and its observer move through the ether.
Imagine that a fight in the center of the room is flashed
on and off and, furthermore, that the walls of the room
are transparent so that the observers, both inside and
outside, can measure the velocity of the fight. If we
ask the two observers what results they expect to ob-
tain, their answers would run something like this:

The outside observer: My CS is designated by the
ether-sea. Light in my CS always has the standard
value. I need not care whether or not the source of
fight or other bodies are moving, for they never carry
my ether-sea with them. My CS is distinguished from
all others and the velocity of fight must have its

1 82 The Evolution of Physics

standard value in this CS, independent of the direction
of die light beam or the motion of its source.

The inside observer: My room moves through the
ether-sea. One of the walls runs away from the light
and the other approaches it. If my room traveled, rela-
tive to the ether-sea, with the velocity of light, then
the light emitted from the center of the room would
never reach the wall running away with the velocity
of light. If the room traveled with a velocity smaller
than that of light, then a wave sent from the center of
the room would reach one of the walls before the
other. The wall moving toward the light wave would
be reached before the one retreating from the light
wave. Therefore, although the source of light is rig-
idly connected with my CS, the velocity of light will
not be the same in all directions. It will be smaller in
the direction of the morion relative to the ether-sea as
the wall runs away, and greater in the opposite direc-
tion as the wall moves toward the wave and tries to
meet it sooner.

Thus, only in the one CS distinguished by the ether-
sea should the velocity of light be equal in all direc-
tions. For other CS moving relatively to the ether-sea
it should depend on the direction in which we are
measuring.

The crucial experiment just considered enables us
to test the theory of motion through the ether-sea. Na-
ture, in fact, places at our disposal a system moving
with a fairly high velocity: the earth in its yearly mo-
tion around the sun. If our assumption is correct, then

Field, Relativity 183

the velocity of light in the direction of the motion of
the earth should differ from the velocity of light in an
opposite direction. The differences can be calculated
and a suitable experimental test devised. In view of the
small time-differences following from the theory, very
ingenious experimental arrangements have to be
thought out. This was done in the famous Michelson-
Morley experiment. The result was a verdict of
“death” to the theory of a calm ether-sea through
which all matter moves. No dependence of the speed
of light upon direction could be found. Not only the
speed of light, but also other field phenomena would
show a dependence on the direction in the moving CS,
if the theory of the ether-sea were assumed. Every ex-
periment has given the same negative result as the
Michelson-Morley one, and never revealed any de-
pendence upon the direction of the motion of the
earth.

The situation grows more and more serious. Two
assumptions have been tried. The first, that moving
bodies carry ether along. The fact that the velocity of
light does not depend on the motion of the source con-
tradicts this assumption. The second, that there exists
one distinguished CS and that moving bodies do not
carry the ether but travel through an ever calm ether-
sea. If this is so, then the Galilean relativity principle
is not valid and the speed of light cannot be the same
in every CS. Again we are in contradiction with ex-
periment.

More artificial theories have been tried out, assum-

184 The Evolution of Physics

ing that the real truth lies somewhere between these
two limiting cases: that the ether is only partially car-
ried by the moving bodies. But they all failed! Every
attempt to explain the electromagnetic phenomena in
moving CS with the help of the motion of the ether,
motion through the ether, or both these motions,
proved unsuccessful.

Thus arose one of the most dramatic situations in
the history of science. All assumptions concerning
ether led nowhere! The experimental verdict was al-
ways negative. Looking back over the development of
physics we see that the ether, soon after its birth, be-
came the enfant terrible ' ’ of the family of physical sub-
stances. First, the construction of a simple mechanical
picture of the ether proved to be impossible and was
discarded. This caused, to a great extent, the break-
down of the mechanical point of view. Second, we had
to give up hope that through the presence of the ether-
sea one CS would be distinguished and lead to the rec-
ogmtion of absolute, and not only relative, motion.
This would have been the only way, besides carrying
the waves, in which ether could mark and justify its
existence. All our attempts to make ether real failed. It
revealed neither its mechanical construction nor abso-
lute motion. Nothing remained of all the properties of
the ether except that for which it was invented, i.e.,
its ability to transmit electromagnetic waves. Our at-
tempts to discover the properties of the ether led to
difficulties and contradictions. After such bad experi-
ences, this is the moment to forget the ether completely

Field, Relativity 185

and to try never to mention its name. We shall say:
our space has the physical property of transmitting
waves, and so omit the use of a word we have decided
to avoid.

The omission of a word from our vocabulary is, of
course, no remedy. Our troubles are indeed much too
profound to be solved in this way!

Let us now write down the facts which have been
sufficiently confirmed by experiment without bother-
ing any more about the “e r” problem.

1 . The velocity of light in empty space always has its
standard value, independent of the motion of the
source or receiver of light.

2. In two CS moving uniformly, relative to each other,
all laws of nature are exactly identical and there is
no way of distinguishing absolute uniform motion.

There are many experiments to confirm these two
statements and not a single one to contradict either of
them. The first statement expresses the constant char-
acter of the velocity of light, the second generalizes the
Galilean relativity principle, formulated for mechan-
ical phenomena, to all happenings in nature.

In mechanics, we have seen: If the velocity of a ma-
terial point is so and so, relative to one CS, then it will
be different in another CS moving uniformly, relative
to the first. This follows from the simple mechanical
transformation principles. They are immediately given
by our intuition (man moving relative to ship and
shore) and apparently nothing can be wrong here! But

1 86

The Evolution of Physics

this transformation law is in contradiction to the con-
stant character of the velocity of light. Or, in other
words, we add a third principle:

3. Positions and velocities are transformed from one
inertial system to another according to the classical
transformation.

The contradiction is then evident. We cannot com-
bine (1), (2), and (3).

The classical transformation seems too obvious and
simple for any attempt to change it. We have already
tried to change (1) and (2) and came to a disagree-
ment with experiment. All theories concerning the

motion of “e r” required an alteration of (1) and

( 2 ) . This was no good. Once more we realize the seri-
ous character of our difficulties. A new clew is needed.
It is supplied by accepting the fundctmental assump-
tions (1) and (2), and, strange though it seems, giving
zip (3). The new clew starts from an analysis of the
most fundamental and primitive concepts; we shall
show how this analysis forces us to change our old
views and removes all our difficulties.

TIME, DISTANCE, RELATIVITY

Our new assumptions are:

1. The velocity of light in vacuo is the same in all CS
moving uniformly, relative to each other.

2. All laws of nature are the same in all CS moving
uniformly, relative to each other.

The relativity theory begins with these two assump-
tions. From now on we shall not use the classical trans-

Field, Relativity 187

formation because we know that it contradicts our
assumptions.

It is essential here, as always in science, to rid our-
selves of deep-rooted, often uncritically repeated, prej-
udices. Since we have seen that changes in ( 1 ) and (2)
lead to contradiction with experiment, we must have
the courage to state their validity clearly and to attack
the one possibly weak point, the way in which posi-
tions and velocities are transformed from one CS to
another. It is our intention to draw conclusions from
(1) and (2), see where and how these assumptions
contradict the classical transformation, and find the
physical meaning of the results obtained.

Once more, the example of the moving room with
outside and inside observers will be used. Again a light
signal is emitted from the center of the room and again
we ask the two men what they expect to observe, as-
suming only our two principles and forgetting what
was previously said concerning the medium through
which the light travels. We quote their answers:

The inside observer: The light signal traveling from
the center of the room will reach the walls simulta-
neously , since all the walls are equally distant from the.
light source and the velocity of light is the same in all
directions.

The outside observer: In my system, the velocity of
light is exactly the same as in that of the observer mov-
ing with the room. It does not matter to me whether
or not the light source moves in my CS since its motion
does not influence the velocity of light. What I see is a

*88 The Evolution of Physics

light signal traveling with a standard speed, the same
in all directions. One of the walls is trying to escape
from and the opposite wall to approach the light signal.
Therefore, the escaping wall will be met by the signal
a little later than the approaching one. Although the
difference will be very slight if the velocity of the
room is small compared with that of light, the light
signal will nevertheless not meet these two opposite
walls, which are perpendicular to the direction of the
motion, quite simultaneously.

Comparing the predictions of our two observers we
find a most astonishing result which flatly contradicts
the apparently well-founded concepts of classical
physics. Two events, i.e., the two light beams reaching
the two walls, are simultaneous for the observer on the
inside, but not for the observer on the outside. In
classical physics, we had one clock, one time flow, for
all observers in all CS. Time, and therefore such words
as “simultaneously,” “sooner,” “later,” had an absolute
meaning independent of any CS. Two events happen-
mg at the same time in one CS happened necessarily
simultaneously in all other CS.

Assumptions (i) and ( 2 ), i.e., the relativity theory,
force us to give up this view. We have described two
events happening at the same time in one CS, but at
different times in another CS. Our task is to understand
this consequence, to understand the meaning of the
sentence: “Two events which are simultaneous in one
CS, may not be simultaneous in another CS.”

What do we mean by “two simultaneous events in

Field, Relativity 1 89

one CS”? Intuitively everyone seems to know the
meaning of this sentence. But let us make up our minds
to be cautious and try to give rigorous definitions, as
we know how dangerous it is to overestimate intuition.
Let us first answer a simple question.

What is a clock?

The primitive subjective feeling of time flow enables
us to order our impressions, to judge that one event
takes place earlier, another later. But to show that the
time interval between two events is 10 seconds, a clock
is needed. By the use of a clock the time concept be-
comes objective. Any physical phenomenon may be
used as a clock, provided it can be exactly repeated as
many times as desired. Taking the interval between the
beginning and the end of such an event as one unit of
time, arbitrary time-intervals may be measured by
repetition of this physical process. All clocks, from the
simple hourglass to the most refined instruments, are
based on this idea. With the hourglass the unit of time
is the interval the sand takes to flow from the upper to
the lower glass. The same physical process can be re-
peated by inverting the glass.

At two distant points we have two perfect clocks,
showing exactly the same time. This statement should
be true regardless of the care with which we verify it.
But what does it really mean? How can we make sure
that distant clocks always show exactly the same time?
One possible method would be to use television. It
should be understood that television is used only as an
example and is not essential to our argument. I could

i9° The Evolution of Physics

stand near one of the clocks and look at a televised
picture of the other. I could then judge whether or not
they showed the same time simultaneously. But this
would not be a good proof. The televised picture is
transmitted through electromagnetic waves and thus
travels with the speed of light. Through television I
see a picture which was sent some very short time be-
fore, whereas on the real clock I see what is taking
place at the present moment. This difficulty can easily
be avoided. I must take television pictures of the two
clocks at a point equally distant from each of them and
observe them from this center point. Then, if the sig-
nals are sent out simultaneously, they will all reach me
at the same instant. If two good clocks observed from
the mid-point of the distance between them always
show the same time, then they are well suited for desig-
nating the time of events at two distant points.

In mechanics we used only one clock. But this was
not very convenient, because we had to take all meas-
urements in the vicinity of this one clock. Looking at
the clock from a distance, for example by television,
we have always to remember that what we see now
really happened earlier, just as we receive light from
the sun eight minutes after it was emitted. We should
have to make corrections, according to our distance
from the clock, in all our time readings.

It is, therefore, inconvenient to have only one clock.
Now, however, as we know how to judge whether
two, or more, clocks show the same time simulta-
neously and run in the same way, we can very well

Field, Relativity 19 1

imagine as many clocks as we like in a given CS. Each
of them will help us to determine the time of the events
happening in its immediate vicinity. The clocks are all
at rest relative to the CS. They are “good” clocks and
are synchronized , which means that they show the
same time simultaneously.

There is nothing especially striking or strange about
the arrangements of our clocks. We are now using
many synchronized clocks instead of only one and can,
therefore, easily judge whether or not two distant
events are simultaneous in a given CS. They are if the
synchronized clocks in their vicinity show the same
time at the instant the events happen. To say that one
of the distant events happens before the other has now
a definite meaning. All this can be judged by the help
of the synchronized clocks at rest in our CS.

This is in agreement with classical physics, and not
one contradiction to the classical transformation has
yet appeared.

For the definition of simultaneous events, the clocks
are synchronized by the help of signals. It is essential
in our arrangement that these signals travel with the
velocity of light, the velocity which plays such a
fundamental role in the theory of relativity.

Since we wish to deal with the important problem
of two CS moving uniformly, relative to each other,
we must consider two rods, each provided with clocks.
The observer in each of the two CS moving relative to
each other now has his own rod with his own set of
clocks rigidly attached.

l 9 2

The Evolution of Physics

When discussing measurements in classical mechan-
ics we used one clock for all CS. Here we have many
clocks in each CS. This difference is unimportant. One
clock was sufficient, but nobody could object to the
use of many, so long as they behave as decent syn-
chronized clocks should.

Now we are approaching the essential point showing
where the classical transformation contradicts the
theory of relativity. What happens when two sets of
clocks are moving uniformly, relative to each other?
The classical physicist would answer: Nothing; they
still have the same rhythm, and we can use moving
as well as resting clocks to indicate time. According to
classical physics, two events simultaneous in one CS
will also be simultaneous in any other CS.

But this is not the only possible answer. We can
equally well imagine a moving clock having a different
rhythm from one at rest. Let us now discuss this pos-
sibility without deciding, for the moment, whether or
not clocks really change their rhythm in motion. What
is meant by the statement that a moving clock changes
its rhythm? Let us assume, for the sake of simplicity,
that we have only one clock in the upper CS and many
in the lower. All the clocks have the same mechanism,
and the lower ones are synchronized, that is, they show
the same time simultaneously. We have drawn three
subsequent positions of the two CS moving relative to
each other. In the first drawing the positions of the
hands of the upper and lower clocks are, by conven-
tion, the same because we arranged them so. All the

Field, Relativity 193

clocks show the same time. In the second drawing, we
see the relative positions of the two CS some time later.

All the clocks in the lower CS show the same time, but
the clock in the upper CS is out of rhythm. The
rhythm is changed and the time differs because the
clock is moving relative to the lower CS. In the third
drawing we see the difference in the positions of the
hands increased with time.

194 T/je Evolution of Physics

An observer at rest in the lower CS would find that
a moving clock changes its rhythm. Certainly the same
result could be found if the clock moved relative to an
observer at rest in the upper CS; in this case there
would have to be many clocks in the upper CS and
only one in the lower. The laws of nature must be the
same in both CS moving relative to each other.

In classical mechanics it was tacitly assumed that a
moving clock does not change its rhythm. This seemed
so obvious that it was hardly worth mentioning. But
nothing should be too obvious; if we wish to be really
careful, we should analyze the assumptions, so far
taken for granted, in physics.

An assumption should not be regarded as unreason-
able simply because it differs from that of classical
physics. We can well imagine that a moving clock
changes its rhythm, so long as the law of this change is
the same for all inertial CS.

Yet another example. Take a yardstick; this means
that a stick is a yard in length as long as it is at rest in a
CS. Now it moves uniformly, sliding along the rod
representing the CS. Will its length still appear to be
one yard? We must know beforehand how to deter-
mine its length. As long as the stick was at rest its ends
coincided with markings one yard apart on the CS.
From this we concluded: the length of the resting stick
is one yard. How are we to measure this stick during
motion? It could be done as follows. At a given mo-
ment two observers simultaneously take snapshots, one
of the origin of the stick and the other of the end. Since

Field, Relativity 195

the pictures are taken simultaneously we can compare
the marks on the CS rod with which the origin and the
end of the moving stick coincide. In this way we deter-
mine its length. There must be two observers to take
note of simultaneous events in different parts of the
given CS. There is no reason to believe that the result
of such measurements will be the same as in the case of
a stick at rest. Since the photographs had to be taken
simultaneously, which is, as we already know, a rela-
tive concept depending on the CS, it seems quite pos-
sible that the results of this measurement will be differ-
ent in different CS moving relative to each other.

We can well imagine that not only does the moving
clock change its rhythm, but also that a moving stick
changes its length, so long as the laws of the changes
are the same for all inertial CS.

We have only been discussing some new possibilities
without giving any justification for assuming them.

We remember: the velocity of light is the same in all
mertial CS. It is impossible to reconcile this fact with
the classical transformation. The circle must be broken
somewhere. Can it not be done just here? Can we not
assume such changes in the rhythm of the moving
clock and in the length of the moving rod that the con-
stancy of the velocity of light will follow directly
from these assumptions? Indeed we can! Here is the
first instance in which the relativity theory and classical
physics differ radically. Our argument can be reversed:
if the velocity of light is the same in all CS, then mov-
ing rods must change their length, moving clocks must

196 The Evolution of Physics

change their rhythm, and the laws governing these
changes are rigorously determined.

There is nothing mysterious or unreasonable in all
this. In classical physics it was always assumed that
clocks in motion and at rest have the same rhythm, that
rods in motion and at rest have the same length. If the
velocity of light is the same in all CS, if the relativity
theory is valid, then we must sacrifice this assumption.
It is difficult to get rid of deep-rooted prejudices, but
there is no other way. From the point of view of the
relativity theory the old concepts seem arbitrary. Why
believe, as we did some pages ago, in absolute time
flowing in the same way for all observers in all CS?
Why believe in unchangeable distance? Time is deter-
mined by clocks, space co-ordinates by rods, and the
result of their determination may depend on the be-
havior of these clocks and rods when in motion. There
is no reason to believe that they will behave in the way
we should like them to. Observation shows, indirectly,
through the phenomena of electromagnetic field, that
a moving clock changes its rhythm, a rod its length,
whereas on the basis of mechanical phenomena we did
not think this happened. We must accept the concept
of relative time in every CS, because it is the best way
out of our difficulties. Further scientific advance, de-
veloping from the theory of relativity, shows that this
new aspect should not be regarded as a malum neces-
sarium, for the merits of the theory are much too
marked.

So far we have tried to show what led to the funda-

Field, Relativity 197

mental assumptions of the relativity theory, and how
the theory forced us to revise and to change the classi-
cal transformation by treating time and space in a new
way. Our aim is to indicate the ideas forming the basis
of a new physical and philosophical view. These ideas
are simple; but in the form in which they have been
formulated here, they are insufficient for arriving at
not only qualitative, but also quantitative conclusions.
We must again use our old method of explaining only
the principal ideas and stating some of the others with-
out proof.

To make clear the difference between the view of
the old physicist, whom we shall call O and who be-
lieves in the classical transformation, and that of the
modem physicist, whom we shall call M and who
knows the relativity theory, we shall imagine a dialogue
between them.

O. I believe in the Galilean relativity principle in
mechanics, because I know that the laws of mechanics
are the same in two CS moving uniformly relative
to each other, or in other words, that these laws are in-
variant with respect to the classical transformation.

M. But the relativity principle must apply to all
events in our external world. Not only the laws of
mechanics but all laws of nature must be the same in
CS moving uniformly, relative to each other.

O. But how can all laws of nature possibly be the
same in CS moving relative to each other? The field
equations, that is, Maxwell’s equations, are not invari-
ant with respect to the classical transformation. This is

198 The Evolution of Physics

clearly shown by the example of the velocity of light.
According to the classical transformation, this velocity
should not be the same in two CS moving relative to
each other.

M. This merely shows that the classical transforma-
tion cannot be applied, that the connection between
two CS must be different; that we may not connect
co-ordinates and velocities as is done in these transfor-
mation laws. We have to substitute new laws and de-
duce them from the fundamental assumptions of the
theory of relativity. Let us not bother about the mathe-
matical expression for this new transformation law,
and be satisfied that it is different from the classical.
We shall call it briefly the Lorentz transformation. It
can be shown that Maxwell’s equations, that is, the
laws of field are invariant with respect to the Lorentz
transformation, just as the laws of mechanics are in-
variant with respect to the classical transformation.
Remember how it was in classical physics. We haii
transformation laws for co-ordinates, transformation
laws for velocities, but the laws of mechanics were the
same for two CS moving uniformly, relative to each
other. We had transformation laws for space, but not
for time, because time was the same in all CS. Here,
however, in the relativity theory, it is different. We
have transformation laws different from the classical
for space, time, and velocity. But again the laws of
nature must be the same in all CS moving uniformly,
relative to each other. The laws of nature must be in-
variant, not, as before, with respect to the classical

Field, Relativity 199

transformation, but with respect to a new type of
transformation, the so-called Lorentz transformation.
In all inertial CS the same laws are valid and the transi-
tion from one CS to another is given by the Lorentz
transformation.

O. I take your word for it, but it would interest me
to know the difference between the classical and
Lorentz transformations.

M. Your question is best answered in the following
way. Quote some of the characteristic features of the
classical transformation and I shall try to explain
whether or not they are preserved in the Lorentz
transformation, and if not, how they are changed.

O. If something happens at some point at some time
in my CS, then the observer in another CS moving uni-
formly, relative to mine, assigns a different number to
the position in which this event occurs, but of course
the same time. We use the same clock in all our CS
and it is immaterial whether or not the clock moves. Is
this also true for you?

M. No, it is not. Every CS must be equipped with
its own clocks at rest, since motion changes the
rhythm. Two observers in two different CS will assign
not only different numbers to the position, but also
different numbers to the time at which this event
happens.

O. This means that the time is no longer an invari-
ant. In the classical transformation it is always the same
time in all CS. In the Lorentz transformation it changes
and somehow behaves like the co-ordinate in the old

200 The Evolution of Physics

transformation. I wonder how it is with distance? Ac-
cording to classical mechanics a rigid rod preserves its
length in motion or at rest. Is this also true now?

M. It is not. In fact, it follows from the Lorentz
transformation that a moving stick contracts in the
direction of the motion and the contraction increases if
the speed increases. The faster a stick moves, the

shorter it appears. But this occurs only in the direction
of the motion. You see in my drawing a moving rod
which shrinks to half its length, when it moves with a
velocity approaching ca. 90 per cent of the velocity of

I

201

Field, Relativity

light. There is no contraction, however, in the direc-
tion perpendicular to the motion, as I have tried to
illustrate in my last drawing.

O. This means that the rhythm of a moving clock
and the length of a moving stick depend on the speed.
But how?

M. The changes become more distinct as the speed
increases. It follows from the Lorentz transformation
that a stick would shrink to nothing if its speed were to
reach that of light. Similarly the rhythm of a moving
clock is slowed down, compared to the clocks it passes
along the rod, and would come to a stop if the clock
were to move with the speed of light, that is, if the
clock is a “good” one.

O. This seems to contradict all our experience. We
know that a car does not become shorter when in mo-
tion and we also know that the driver can always com-
pare his “good” watch with those he passes on the way,
finding that they agree fairly well, contrary to your
statement.

M. This is certainly true. But these mechanical ve-
locities are all very small compared to that of light, and
it is, therefore, ridiculous to apply relativity to these
phenomena. Every car driver can safely apply classical
physics even if he increases his speed a hundred thou-
sand times. We could only expect disagreement be-
tween experiment and the classical transformation with
velocities approaching that of light. Only with very
great velocities can the validity of the Lorentz trans-
formation be tested.

202 The Evolution of Physics

O. But there is yet another difficulty. According to
mechanics I can imagine bodies with velocities even
greater than that of light. A body moving with the
velocity of light relative to a floating ship moves with a
velocity greater than that of light relative to the shore.
What will happen to the stick which shrank to nothing
when its velocity was that of light? We can hardly ex-
pect a negative length if the velocity is greater than that
of light.

M. There is really no reason for such sarcasm! From
the point of view of the relativity theory a material
body cannot have a velocity greater than that of light.
The velocity of light forms the upper limit of veloc-
ities for all material bodies. If the speed of a body is
equal to that of light relative to a ship then it will also
be equal to that of light relative to the shore. The sim-
ple mechanical law of adding and subtracting veloc-
ities is no longer valid or, more precisely, is only ap-
proximately valid for small velocities, but not for those
near the velocity of light. The number expressing the
velocity of light appears explicitly in the Lorentz trans-
formation, and plays the role of a limiting case, like the
infinite velocity in classical mechanics. This more gen-
eral theory does not contradict the classical transfor-
mation and classical mechanics. On the contrary, we
regain the old concepts as a limiting case when the ve-
locities are small. From the point of view of the new
theory it is clear in which cases classical physics is
valid and wherein its limitations lie. It would be just as
ridiculous to apply the theory of relativity to the mo-

203

Field, Relativity

tion of cars, ships, and trains as to use a calculating
machine where a multiplication table would be suffi-
cient.

RELATTV ITY AND MECHANICS

The relativity theory arose from necessity, from
serious and deep contradictions in the old theory from
which there seemed no escape. The strength of the
new theory lies in the consistency and simplicity with
which it solves all these difficulties, using only a few
very convincing assumptions.

Although the theory arose from the field problem, it
has to embrace all physical laws. A difficulty seems to
appear here. The field laws on the one hand and the
mechanical laws on the other are of quite different
kinds. The equations of electromagnetic field are in-
variant with respect to the Lorentz transformation and
the mechanical equations are invariant with respect to
the classical transformation. But the relativity theory
claims that all laws of nature must be invariant with
respect to the Lorentz and not to the classical trans-
formation. The latter is only a special, limiting case of
the Lorentz transformation when the relative veloci-
ties of two CS are very small. If this is so, classical
mechanics must change in order to conform with the
demand of invariance with respect to the Lorentz
transformation. Or, in other words, classical mechanics
cannot be valid if the velocities approach that of light.
Only one transformation from one CS to another can
exist, namely, the Lorentz transformation.

204 The Evolution of Physics

It was simple to change classical mechanics in such a
way that it contradicted neither the relativity theory
nor the wealth of material obtained by observation and
explained by classical mechanics. The old mechanics is
valid for small velocities and forms the limiting case of
the new one.

It would be interesting to consider some instance of
a change in classical mechanics introduced by the rela-
tivity theory. This might, perhaps, lead us to some
conclusions which could be proved or disproved by
experiment.

Let us assume a body, having a definite mass, moving
along a straight line, and acted upon by an external
force in the direction of the motion. The force, as we
know, is proportional to the change of velocity. Or, to
be more explicit, it does not matter whether a given
body increases its velocity in one second from ioo to
ioi feet per second, or from ioo miles to ioo miles and
one foot per second or from 180,000 miles to 180,000
miles and one foot per second. The force acting upon
a particular body is always the same for the same
change of velocity in the same time.

Is this sentence true from the point of view of the
relativity theory ? By no means! This law is valid only
for small velocities. What, according to the relativity
theory, is the law for great velocities, approaching that
of light? If the velocity is great, extremely strong
forces are required to increase it. It is not at all the
same thing to increase by one foot per second a veloc-
ity of about 100 feet per second or a velocity ap-

2°5

Field, Relativity

proaching that of light. The nearer a velocity is to that
of light the more difficult it is to increase. When a
velocity is equal to that of light it is impossible to in-
crease it further. Thus, the changes brought about by
the relativity theory are not surprising. The velocity of
light is the upper limit for all velocities. No finite force,
no matter how great, can cause an increase in speed
beyond this limit. In place of the old mechanical law
connecting force and change of velocity, a more com-
plicated one appears. From our new point of view clas-
sical mechanics is simple because in nearly all observa-
tions we deal with velocities much smaller than that of
light.

A body at rest has a definite mass, called the rest mass.
We know from mechanics that every body resists a
change in its motion; the greater the mass, the stronger
the resistance, and the weaker the mass, the weaker the
resistance. But in the relativity theory, we have some-
thing more. Not only does a body resist a change more
strongly if the rest mass is greater, but also if its veloc-
ity is greater. Bodies with velocities approaching that
of light would offer a very strong resistance to external
forces. In classical mechanics the resistance of a given
body was something unchangeable, characterized by
its mass alone. In the relativity theory it depends on
both rest mass and velocity. The resistance becomes in-
finitely great as the velocity approaches that of light.

The results just quoted enable us to put the theory to
the test of experiment. Do projectiles with a velocity
approaching that of light resist the action of an ex-

20 6

The Evolution of Physics

temal force as predicted by the theory? Since the state-
ments of the relativity theory have, in this respect, a
quantitative character, we could confirm or disprove
the theory if we could realize projectiles having a speed
approaching that of light.

Indeed, we find in nature projectiles with such veloc-
ities. Atoms of radioactive matter, radium for instance,
act as batteries which fire projectiles with enormous
velocities. Without going into detail we can quote
only one of the very important views of modem phys-
ics and chemistry. All matter in the universe is made up
of elementary particles of only a few kinds. It is like
seeing in one town buildings of different sizes, con-
struction and architecture, but from shack to sky-
scraper only very few different kinds of bricks were
used, the same in all the buildings. So all known ele-
ments of our material world, from hydrogen the light-
est, to uranium the heaviest, are built of the same kinds

bricks, that is, the same kinds of elementary par-
ticles. The heaviest elements, the most complicated
buildings, are unstable and they disintegrate or, as we
say, are radioactive. Some of the bricks, that is, the ele-
mentary particles of which the radioactive atoms are
constructed, are sometimes thrown out with a very
great velocity, approaching that of light. An atom of
an element, say radium, according to our present
views, confirmed by numerous experiments, is a com-
plicated structure, and radioactive disintegration is one
of those phenomena in which the composition of atoms

Field, Relativity 207

from still simpler bricks, the elementary particles, is
revealed.

By very ingenious and intricate experiments we can
find out how the particles resist the action of an ex-
ternal force. The experiments show that the resistance
offered by these particles depends on the velocity, in
the way foreseen by the theory of relativity. In many
other cases, where the dependence of the resistance
upon the velocity could be detected, there was com-
plete agreement between theory and experiment. We
see once more the essential features of creative work
in science: prediction of certain facts by theory and
their confirmation by experiment.

This result suggests a further important generaliza-
tion. A body at rest has mass but no kinetic energy,
that is, energy of motion. A moving body has both
mass and kinetic energy. It resists change of velocity
more strongly than the resting body. It seems as though
the kinetic energy of the moving body increases its
resistance. If two bodies have the same rest mass, the
one with the greater kinetic energy resists the action of
an external force more strongly.

Imagine a box containing balls, with the box as well
as the balls at rest in our CS. To move it, to increase its
velocity, some force is required. But will the same
force increase the velocity by the same amount in the
same time with the balls moving about quickly and in
all directions inside the box, like the molecules of a gas,
with an average speed approaching that of light? A
greater force will now be necessary because of the in-

208 The Evolution of Physics

creased kinetic energy of the balls, strengthening the
resistance of the box. Energy, at any rate kinetic
energy, resists motion in the same way as ponderable
masses. Is this also true of all kinds of energy?

The theory of relativity deduces, from its funda-
mental assumption, a clear and convincing answer to
this question, an answer again of a quantitative char-
acter: all energy resists change of motion; all energy
behaves like matter; a piece of iron weighs more when
red-hot than when cool; radiation traveling through
space and emitted from the sun contains energy and
therefore has mass; the sun and all radiating stars lose
mass by emitting radiation. This conclusion, quite gen-
eral in character, is an important achievement of the
theory of relativity and fits all facts upon which it has
been tested.

Classical physics introduced two substances: matter
and energy. The first had weight, but the second was
weightless. In classical physics we had two conserva-
tion laws: one for matter, the other for energy. We
have already asked whether modem physics still holds
this view of two substances and the two conservation
laws. The answer is: “No.” According to the theory
of relativity, there is no essential distinction between
mass and energy. Energy has mass and mass represents
energy. Instead of two conservation laws we have only
one, that of mass-energy. This new view proved very
successful and fruitful in the further development of
physics.

How is it that this fact of energy having mass and

Field, Relativity 209

mass representing energy remained for so long ob-
scured? Is the weight of a piece of hot iron greater
than that of a cold piece? The answer to this question is
now “yes,” but on p. 43 it was “no.” The pages be-
tween these two answers are certainly not sufficient to
cover this contradiction.

The difficulty confronting us here is of the same
kind as we have met before. The variation of mass pre-
dicted by the theory of relativity is immeasurably small
and cannot be detected by direct weighing on even the
most sensitive scales. The proof that energy is not
weightless can be gained in many very conclusive, but
indirect, ways.

The reason for this lack of immediate evidence is the
very small rate of exchange between matter and en-
ergy. Compared to mass, energy is like a depreciated
currency compared to one of high value. An example
will make this clear. The quantity of heat able to con-
vert thirty thousand tons of water into steam would
weigh about one gram! Energy was regarded as
weightless for so long simply because the mass which
it represents is so small.

The old energy-substance is the second victim of
the theory of relativity. The first was the medium
through which light waves were propagated.

The influence of the theory of relativity goes far
beyond the problem from which it arose. It removes
the difficulties and contradictions of the field theory;
it formulates more general mechanical laws; it replaces

210

The Evolution of Physics

two conservation laws by one; it changes our classical
concept of absolute time. Its validity is not restricted
to one domain of physics; it forms a general framework
embracing all phenomena of nature.

THE TIME-SPACE CONTINUUM

“The French revolution began in Paris on the 14th
of July, 1789.” In this sentence the place and time of
an event are stated. Hearing this statement for the first
time one who does not know what “Paris” means could
be taught: it is a city on our earth .situated in long. 2°
East and lat. 49 0 North. The two numbers would then
characterize the place, and “14th of July, 1789” the
time, at which the event took place. In physics, much
more than in history, the exact characterization of
when and where an event takes place is very impor-
tant, because these data form the basis for a quantita-
tive description.

For the sake of simplicity, we considered previously
only motion along a straight line. A rigid rod with an
origin but no end point was our CS. Let us keep this
restriction. Take different points on the rod; their
positions can be characterized by one number only, by
the co-ordinate of the point. To say the co-ordinate of
a point is 7.586 feet means that its distance is 7.586 feet
from the origin of the rod. If, on the contrary, some-
one gives me any number and a unit, I can always find
a point on the rod corresponding to this number. We
can state: a definite point on the rod corresponds to

21 I

Field, Relativity

every number, and a definite number corresponds to
every point. This fact is expressed by mathematicians
in the following sentence: all points on the rod form a
one-dimensional continuum. There exists a point arbi-
trarily near every point on the rod. We can connect
two distant points on the rod by steps as small as we
wish. Thus the arbitrary smallness of the steps con-
necting distant points is characteristic of the con-
tinuum.

Now another example. We have a plane, or, if you
prefer something more concrete, the surface of a rec-
tangular table. The position of a point on this table
can be characterized by two numbers and not, as be-
fore, by one. The two numbers are the distances from
two perpendicular edges of the table. Not one num-

ber, but a pair of numbers corresponds to every point
on the plane; a definite point corresponds to every pair
of numbers. In other words: the plane is a two-dimen-
sional continuum. There exist points arbitrarily near
every point on the plane. Two distant points can be
connected by a curve divided into steps as small as
we wish. Thus the arbitrary smallness of the steps con-
necting two distant points, each of which can be rep-

212

The Evolution of Physics

resented by two numbers, is again characteristic of a
two-dimensional continuum.

One more example. Imagine that you wish to re-
gard your room as your CS. This means that you want
to describe all positions with respect to the rigid walls
of the room. The position of the end point of the
lamp, if the lamp is at rest, can be described by three
numbers: two of them determine the distance from
two perpendicular walls, and the third that from the
floor or ceiling. Three definite numbers correspond to

every point of the space; a definite point in space cor-
responds to every three numbers. This is expressed by
the sentence: Our space is a three-dimensional con-
tinuum. There exist points very near every point of
the space. Again the arbitrary smallness of the steps
connecting the distant points, each of them repre-
sented by three numbers, is characteristic of a three-
dimensional continuum.

But all this is scarcely physics. To return to physics,
the motion of material particles must be considered.
To observe and predict events in nature we must con-

Field, Relativity 2 1 3

sider not only the place but also the time of physical
happenings. Let us again take a very simple example.

A small stone, which can be regarded as a particle,
is dropped from a tower. Imagine the tower 256 feet
high. Since Galileo’s time we have been able to pre-
dict the co-ordinate of the stone at any arbitrary in-
stant after it was dropped. Here is a “timetable” de-
scribing the positions of the stone after o, 1, 2, 3, and 4
seconds.

Time in
seconds

Elevation from
the ground in feet

0

256

1

240

2

192

3

1 12

4

O

Five events are registered in our “timetable,” each rep-
resented by two numbers, the time and space co-ordi-
nates of each event. The first event is the dropping of
the stone from 256 feet above the ground at the zero
second. The second event is the coincidence of the
stone with our rigid rod (the tower) at 240 feet above
the ground. This happens after the first second. The
last event is the coincidence of the stone with the
earth.

We could represent the knowledge gained from our
“timetable” in a different way. We could represent
the five pairs of numbers in the “timetable” as five
points on a surface. Let us first establish a scale. One

2I 4

The Evolution of Physics

segment will correspond to a foot and another to a
second. For example:

100 Ft. I See.

We then draw two perpendicular lines, calling the
horizontal one, say, the time axis and the vertical one
the space axis. We see immediately that our “time-
table” can be represented by five points in our time-
space plane.

Feet

Seconds

The distances of the points from the space axis rep-
resent the time co-ordinates as registered in the first
column of our “timetable,” and the distances from the
time axis their space co-ordinates.

Exactly the same thing is expressed in two different
ways: by the “timetable” and by the points on the
plane. Each can be constructed from the other. The

Field, Relativity 215

choice between these two representations is merely a
matter of taste, for they are, in fact, equivalent.

Let us now go one step further. Imagine a better
“timetable” giving the positions not for every second,
but for, say, every hundredth or thousandth of a sec-
ond. We shall then have very many points on our
time-space plane. Finally, if the position is given for
every instant or, as the mathematicians say, if the space
co-ordinate is given as a function of time, then our set
of points becomes a continuous line. Our next draw-
ing therefore represents not just a fragment as before,
but a complete knowledge of the motion.

Feet

The motion along the rigid rod (the tower), the mo-
tion in a one-dimensional space, is here represented as
a curve in a two-dimensional time-space continuum.
To every point in our time-space continuum there
corresponds a pair of numbers, one of which denotes

21 6

The Evolution of Physics

the time, and the other the space, co-ordinate. Con-
versely: a definite point in our time-space plane cor-
responds to every pan* of numbers characterizing an
event. Two adjacent points represent two events, two
happenings, at slightly different places and at slightly
different instants.

You could argue against our representation thus:
there is little sense in representing a unit of time by a
segment, in combining it mechanically with the space,
forming the two-dimensional continuum from the two
one-dimensional continua. But you would then have
to protest just as strongly against all the graphs repre-
senting, for example, the change of temperature in
New York City during last summer, or against those
representing the changes in the cost of living during
the last few years, since the very same method is used
in each of these cases. In the temperature graphs the
one-dimensional temperature continuum is combined
with the one-dimensional time continuum into the
two-dimensional temperature-time continuum.

Let us return to the particle dropped from a 2 56-
foot tower. Our graphic picture of motion is a useful
convention since it characterizes the position of the
particle at an arbitrary instant. Knowing how the par-
ticle moves, we should like to picture its motion once
more. We can do this in two different ways.

We remember the picture of the particle changing
its position with time in the one-dimensional space.
We picture the motion as a sequence of events in the
one-dimensional space continuum. We do not mix

Field, Relativity 217

time and space, using a dynamic picture in which po-
sitions change with time.

But we can picture the same motion in a different
way. We can form a static picture, considering the
curve in the two-dimensional time-space continuum.
Now the motion is represented as something which is,
which exists in the two-dimensional time-space con-
tinuum, and not as something which changes in the
one-dimensional space continuum.

Both these pictures are exactly equivalent and pre-
ferring one to the other is merely a matter of conven-
tion and taste.

Nothing that has been said here about the two pic-
tures of the motion has anything whatever to do with
the relativity theory. Both representations can be used
with equal right, though classical physics favored
rather the dynamic picture describing motion as hap-
penings in space and not as existing in time-space. But
the relativity theory changed this view. It was dis-
tinctly in favor of the static picture and found in this
representation of motion as something existing in time-
space a more convenient and more objective picture
of reality. We still have to answer the question: why
are these two pictures, equivalent from the point of
view of classical physics, not equivalent from the
point of view of the relativity theory?

The answer will be understood if two CS moving
uniformly, relative to each other, are again taken into
account.

According to classical physics, observers in two CS

2 1 8

The Evolution of Physics

moving uniformly, relative to each other, will assign
different space co-ordinates, but the same time co-
ordinate, to a certain event. Thus in our example, the
coincidence of the particle with the earth is character-
ized in our chosen CS by the time co-ordinate “4” and
by the space co-ordinate “o.” According to classical
mechanics, the stone will still reach the earth after
four seconds for an observer moving uniformly, rela-
tive to the chosen CS. But this observer will refer the
distance to his CS and will, in general, connect dif-
ferent space co-ordinates with the event of collision,
although the time co-ordinate will be the same for him
and for all other observers moving uniformly, relative
to each other. Classical physics knows only an “ab-
solute” time flow for all observers. For every CS the
two-dimensional continuum can be split into two one-
dimensional continua: time and space. Because of the
“absolute” character of time, the transition from the
“static” to the “dynamic” picture of motion has an
objective meaning in classical physics.

But we have already allowed ourselves to be con-
vinced that the classical transformation must not be
used in physics generally. From a practical point of
view it is still good for small velocities, but not for
settling fundamental physical questions.

According to the relativity theory the time of the
collision of the stone with the earth will not be the
same for all observers. The time co-ordinate and the
space co-ordinate will be different in two CS, and the
change in the time co-ordinate will be quite distinct

Field, Relativity 219

if the relative velocity is close to that of light. The
two-dimensional continuum cannot be split into two
one-dimensional continua as in classical physics. We
must not consider space and time separately in deter-
mining the time-space co-ordinates in another CS. The
splitting of the two-dimensional continuum into two
one-dimensional ones seems, from the point of view
of the relativity theory, to be an arbitrary procedure
without objective meaning.

It will be simple to generalize all that we have just
said for the case of motion not restricted to a straight
line. Indeed, not two, but four, numbers must be used
to describe events in nature. Our physical space as
conceived through objects and their motion has three
dimensions, and positions are characterized by three
numbers. The instant of an event is the fourth num-
ber. Four definite numbers correspond to every event;
a definite event corresponds to any four numbers.
Therefore: The world of events forms a four-dimen-
sional continuum. There is nothing mysterious about
this, and the last sentence is equally true for classical
physics and the relativity theory. Again a difference is
revealed when two CS moving relatively to each other
are considered. The room is moving, and the observ-
ers inside and outside determine the time-space co-
ordinates of the same events. Again the classical phys-
icist splits the four-dimensional continua into the
three-dimensional spaces and the one-dimensional
time-continuum. The old physicist bothers only about
space transformation, as time is absolute for him. He

220

The Evolution of Physics

finds the splitting of the four-dimensional world-con-
tinua into space and time natural and convenient. But
from the point of view of the relativity theory, time
as well as space is changed by passing from one CS to
another, and the Lorentz transformation considers the
transformation properties of the four-dimensional
time-space continuum of our four-dimensional world
of events.

The world of events can be described dynamically
by a picture changing in time and thrown onto the
background of the three-dimensional space. But it can
also be described by a static picture thrown onto the
background of a four-dimensional time-space con-
tinuum. From the point of view of classical physics
the two pictures, the dynamic and the static, are
equivalent. But from the point of view of the relativ-
ity theory the static picture is the more convenient
and the more objective.

Even in the relativity theory we can still use the
dynamic picture if we prefer it. But we must remem-
ber that this division into time and space has no ob-
jective meaning since time is no longer “absolute.”
We shall still use the “dynamic” and not the “static”
language in the following pages, bearing in mind its
limitations.

GENERAL RELATIVITY

There still remains one point to be cleared up. One
of the most fundamental questions has not been set-
tled as yet: does an inertial system exist? We have

221

Field, Relativity

learned something about the laws of nature, their in-
variance with respect to the Lorentz transformation,
and their validity for all inertial systems moving uni-
formly, relative to each other. We have the laws but
do not know the frame to which to refer them.

In order to be more aware of this difficulty, let us
interview the classical physicist and ask him some sim-
ple questions:

“What is an inertial system?”

“It is a CS in which the laws of mechanics are valid.
A body on which no external forces are acting moves
uniformly in such a CS. This property thus enables us
to distinguish an inertial CS from any other.”

“But what does it mean to say that no forces are
acting on a body?”

“It simply means that the body moves uniformly in
an inertial CS.”

Here we could once more put the question: “What
is an inertial CS?” But since there is little hope of ob-
taining an answer differing from the above, let us try to
gain some concrete information by changing the ques-
tion:

“Is a CS rigidly connected with the earth an iner-
tial one?”

“No, because the laws of mechanics are not rigor-
ously valid on the earth, due to its rotation. A CS
rigidly connected with the sun can be regarded for
many problems as an inertial CS; but when we speak
of the rotating sun, we again understand that a CS

222 The Evolution of Physics

connected with it cannot be regarded as strictly in-
ertial.”

“Then what, concretely, is your inertial CS, and
how is its state of motion to be chosen?”

“It is merely a useful fiction and I have no idea how
to realize it. If I could only get far away from all mate-
rial bodies and free myself from all external influences,
my CS would then be inertial.”

“But what do you mean by a CS free from all ex-
ternal influences?”

“I mean that the CS is inertial.”

Once more we are back at our initial question!

Our interview reveals a grave difficulty in classical
physics. We have laws, but do not know what frame
to refer them to, and our whole physical structure
seems to be built on sand.

We can approach this same difficulty from a differ-
ent point of view. Try to imagine that there is only
one body, forming our CS, in the entire universe. This
body begins to rotate. According to classical me-
chanics, the physical laws for a rotating body are dif-
ferent from those for a non-rotating body. If the
inertial principle is valid in one case it is not valid
in the other. But all this sounds very suspicious. Is it
permissible to consider the motion of only one body
in the entire universe? By the motion of a body we
always mean its change of position in relation to a sec-
ond body. It is, therefore, contrary to common sense
to speak about the motion of only one body. Classical
mechanics and common sense disagree violently on

Field, Relativity 223

this point. Newton’s recipe is: if the inertial principle
is valid, then the CS is either at rest or in uniform
motion. If the inertial principle is invalid, then the
body is in nonuniform motion. Thus, our verdict of
motion or rest depends upon whether or not all the
physical laws are applicable to a given CS.

Take two bodies, the sun and the earth, for in-
stance. The motion we observe is again relative. It can
be described by connecting the CS with either the
earth or the sun. From this point of view, Copernicus’
great achievement lies in transferring the CS from
the earth to the sun. But as motion is relative and any
frame of reference can be used, there seems to be no
reason for favoring one CS rather than the other.

Physics again intervenes and changes our common-
sense point of view. The CS connected with the sun
resembles an inertial system more than that connected
with the earth. The physical laws should be applied
to Copernicus’ CS rather than to Ptolemy’s. The great-
ness of Copernicus’ discovery can be appreciated only
from the physical point of view. It illustrates the great
advantage of using a CS connected rigidly with the
sun for describing the motion of planets.

No absolute uniform motion exists in classical phys-
ics. If two CS are moving uniformly, relative to each
other, then there is no sense in saying, “This CS is
at rest and the other is moving.” But if two CS are mov-
ing non-uniformly, relative to each other, then there
is very good reason for saying, “This body moves and
the other is at rest (or moves uniformly).” Absolute

224 The Evolution of Physics

motion has here a very definite meaning. There is, at
this point, a wide gulf between common sense and clas-
sical physics. The difficulties mentioned, that of an
inertial system and that of absolute motion, are strictly
connected with each other. Absolute motion is made
possible only by the idea of an inertial system, for
which the laws of nature are valid.

It may seem as though there is no way out of these
difficulties, as though no physical theory can avoid
them. Their root lies in the validity of the laws of
nature for a special class of CS only, the inertial. The
possibility of solving these difficulties depends on the
answer to the following question. Can we formulate
physical laws so that they are valid for all CS, not only
those moving uniformly, but also those moving quite
arbitrarily, relative to each other? If this can be done,
our difficulties will be over. We shall then be able to
apply the laws of nature to any CS. The struggle, so
violent in the early days of science, between the views
of Ptolemy and Copernicus would then be quite mean-
ingless. Either CS could be used with equal justifica-
tion. The two sentences, “the sun is at rest and the
earth moves,” or “the sun moves and the earth is at
rest,” would simply mean two different conventions
concerning two different CS.

Could we build a real relativistic physics valid in
all CS; a physics in which there would be no place
for absolute, but only for relative motion? This is in-
deed possible!

We have at least one indication, though a very weak

Field, Relativity 225

one, of how to build the new physics. Really relativis-
tic physics must apply to all CS and, therefore, also
to the special case of the inertial CS. We already know
the laws for this inertial CS. The new general laws valid
for all CS must, in the special case of the inertial
system, reduce to the old, known laws.

The problem of formulating physical laws for every
CS was solved by the so-called general relativity the-
ory, the previous theory, applying only to inertial
systems, is called the special relativity theory. The two
theories cannot, of course, contradict each other, since
we must always include the old laws of the special
relativity theory in the general laws for an inertial
system. But just as the inertial CS was previously the
only one for which physical laws were formulated, so
now it will form the special limiting case, as all CS
moving arbitrarily, relative to each other, are permis-
sible.

This is the program for the general theory of rela-
tivity. But in sketching the way in which it was ac-
complished we must be even vaguer than we have been
so far. New difficulties arising in the development of
science force our theory to become more and more
abstract. Unexpected adventures still await us. But our
final aim is always a better understanding of reality.
Links are added to the chain of logic connecting
theory and observation. To clear the way leading from
theory to experiment of unnecessary and artificial as-
sumptions, to embrace an ever-wider region of facts,
we must make the chain longer and longer. The sim-

226

The Evolution of Physics

pier and more fundamental our assumptions become,
the more intricate is our mathematical tool of reason-
ing; the way from theory to observation becomes
longer, more subtle, and more complicated. Although
it sounds paradoxical, we could say: Modem physics
is simpler than the old physics and seems, therefore,
more difficult and intricate. The simpler our picture
of the external world and the more facts it embraces,
the stronger it reflects in our minds the harmony of
the universe.

Our new idea is simple: to build a physics valid
for all CS. Its fulfillment brings formal complications
and forces us to use mathematical tools different from
those so far employed in physics. We shall show here
only the connection between the fulfillment of this
program and two principal problems: gravitation
and geometry.

OUTSIDE AND INSIDE THE ELEVATOR

The law of inertia marks the first great advance in
physics; in fact, its real beginning. It was gained by the
contemplation of an idealized experiment, a body mov-
ing forever with no friction nor any other external
forces acting. From this example and later from many
others, we recognized the importance of the idealized
experiment created by thought. Here again, idealized
experiments will be discussed. Although these may
sound very fantastic they will, nevertheless, help us to
understand as much about relativity as is possible by
our simple methods.

Field, Relativity 227

We had previously the idealized experiments with a
uniformly moving room. Here, for a change, we shall
have a falling elevator.

Imagine a great elevator at the top of a skyscraper
much higher than any real one. Suddenly the cable
supporting the elevator breaks, and the elevator falls
freely toward the ground. Observers in the elevator
are performing experiments during the fall. In describ-
ing them, we need not bother about air resistance or
friction, for we may disregard their existence under
our idealized conditions. One of the observers takes a
handkerchief and a watch from his pocket and drops
them. What happens to these two bodies? For the out-
side observer, who is looking through the window of
the elevator, both handkerchief and watch fall toward
the ground in exactly the same way, with the same
acceleration. We remember that the acceleration of a
falling body is quite independent of its mass and that
it was this fact which revealed the equality of gravita-
tional and inertial mass (p. 37). We also remember that
the equality of the two masses, gravitational and in-
ertial, was quite accidental from the point of view
of classical mechanics and played no role in its struc-
ture. Here, however, this equality reflected in the equal
acceleration of all falling bodies is essential and forms
the basis of our whole argument.

Let us return to our falling handkerchief and watch;
for the outside observer they are both falling with the
same acceleration. But so is the elevator, with its walls,
ceiling, and floor. Therefore: the distance between the

228 The Evolution of Physics

two bodies and the floor will not change. For the in-
side observer the two bodies remain exactly where
they were when he let them go. The inside observer
may ignore the gravitational field, since its source lies
outside his CS. He finds that no forces inside the ele-
vator act upon the two bodies, and so they are at
rest, just as if they were in an inertial CS. Strange
things happen in the elevator! If the observer pushes
a body in any direction, up or down for instance, it
always moves uniformly so long as it does not collide
with the ceiling or the floor of the elevator. Briefly
speaking, the laws of classical mechanics are valid for
the observer inside the elevator. All bodies behave in
the way expected by the law of inertia. Our new CS
rigidly connected with the freely falling elevator dif-
fers from the inertial CS in only one respect. In an
inertial CS, a moving body on which no forces are
acting will move uniformly forever. The inertial CS as
represented in classical physics is neither limited in
space nor time. The case of the observer in our elevator
is, however, different. The inertial character of his CS
is limited in space and time. Sooner or later the uni-
formly moving body will collide with the wall of the
elevator, destroying the uniform motion. Sooner or
later the whole elevator will collide with the earth
destroying the observers and their experiments. The
CS is only a “pocket edition” of a real inertial CS.

This local character of the CS is quite essential. If
our imaginary elevator were to reach from the North
Pole to the Equator, with the handkerchief placed over

Field, Relativity 229

the North Pole and the watch over the Equator, then,
for the outside observer, the two bodies would not
have the same acceleration; they would not be at rest
relative to each other. Our whole argument would
fail! The dimensions of the elevator must be limited
so that the equality of acceleration of all bodies rela-
tive to the outside observer may be assumed.

With this restriction, the CS takes on an inertial
character for the inside observer. We can at least indi-
cate a CS in which all the physical laws are valid, even
though it is limited in time and space. If we imagine
another CS, another elevator moving uniformly, rela-
tive to the one falling freely, then both these CS will
be locally inertial. All laws are exactly the same in both.
The transition from one to the other is given by the
Lorentz transformation.

Let us see in what way both the observers, outside
and inside, describe what takes place in the elevator.

The outside observer notices the motion of the ele-
vator and of all bodies in the elevator, and finds them
in agreement with Newton’s gravitational law. For
him, the motion is not uniform, but accelerated, be-
cause of the action of the gravitational field of the
earth.

However, a generation of physicists bom and
brought up in the elevator would reason quite differ-
ently. They would believe themselves in possession of
an inertial system and would refer all laws of nature to
their elevator, stating with justification that the laws
take on a specially simple form in their CS. It would

230 The Evolution of Physics

be natural for them to assume their elevator at rest and
their CS the inertial one.

It is impossible to settle the differences between the
outside and the inside observers. Each of them could
claim the right to refer all events to his CS. Both de-
scriptions of events could be made equally consistent.

We see from this example that a consistent descrip-
tion of physical phenomena in two different CS is pos-
sible, even if they are not moving uniformly, relative
to each other. But for such a description we must take
into account gravitation, building so to speak, the
“bridge” which effects a transition from one CS to the
other. The gravitational field exists for the outside ob-
server; it does not for the inside observer. Accelerated
motion of the elevator in the gravitational field exists
for the outside observer, rest and absence of the gravi-
tational field for the inside observer. But the “bridge,”
the gravitational field, making the description in both
CS possible, rests on one very important pillar: the
equivalence of gravitational and inertial mass. Without
this clew, unnoticed in classical mechanics, our present
argument would fail completely.

Now for a somewhat different idealized experiment.
There is, let us assume, an inertial CS, in which the
law of inertia is valid. We have already described what
happens in an elevator resting in such an inertial CS.
But we now change our picture. Someone outside has
fastened a rope to the elevator and is pulling, with a
constant force, in the direction indicated in our draw-
ing. It is immaterial how this is done. Since the laws of

Field, Relativity z 3 1

mechanics are valid in this CS, the whole elevator
moves with a constant acceleration in the direction of
the motion. Again we shall listen to the explanation of

phenomena going on in the elevator and given by both
the outside and inside observers.

The outside observer: My CS is an inertial one. The
elevator moves with constant acceleration, because a
constant force is acting. The observers inside are in
absolute motion, for them the laws of mechanics are
invalid. They do not find that bodies, on which no
forces are acting, are at rest. If a body is left free, it
soon collides with the floor of the elevator, since the
floor moves upward toward the body. This happens
exactly in the same way for a watch and for a handker-
chief. It seems very strange to me that the observer
inside the elevator must always be on the “floor” be-
cause as soon as he jumps, the floor will reach him
again.

2 3 2

The Evolution of Thy sics

The inside observer: I do not see any reason for be-
lieving that my elevator is in absolute motion. I agree
that my CS, rigidly connected with my elevator, is not
really inertial, but I do not believe that it has anything
to do with absolute motion. My watch, my handker-
chief, and all bodies are falling because the whole ele-
vator is in a gravitational field. I notice exactly the
same kinds of motion as the man on the earth. He
explains them very simply by the action of a gravita-
tional field. The same holds good for me.

These two descriptions, one by the outside, the other
by the inside, observer, are quite consistent, and there is
no possibility of deciding which of them is right. We
may assume either one of them for the description of
phenomena in the elevator: either nonuniform mo-
tion and absence of a gravitational field with the out-
side observer, or rest and the presence of a gravitational
field with the inside observer.

The outside observer may assume that the elevator
is in “absolute” nonuniform motion. But a motion
which is wiped out by the assumption of an acting
gravitational field cannot be regarded as absolute mo-
tion.

There is, possibly, a way out of the ambiguity of two
such different descriptions, and a decision in favor of
one against the other could perhaps be made. Imagine
that a light ray enters the elevator horizontally through
a side window and reaches the opposite wall after a
very short time. Again let us see how the path of the
light would be predicted by the two observers.

Field, Relativity

2 33

The outside observer, believing in accelerated mo-
tion of the elevator, would argue: The light ray enters
the window and moves horizontally, along a straight
line and with a constant velocity, toward the opposite
wall. But the elevator moves upward and during the
time in which the light travels toward the wall, the
elevator changes its position. Therefore, the ray will
meet a point not exactly opposite its point of entrance,
but a little below. The difference will be very slight,
but it exists nevertheless, and the light ray travels, rela-
tive to the elevator, not along a straight, but along a

slightly curved line. The difference is due to the dis-
tance covered by the elevator during the time the ray
is crossing the interior.

T he inside observer, who believes in the gravitational
field acting on all objects in his elevator, would say:
there is no accelerated motion of the elevator, but only
the action of the gravitational field. A beam of light is
weightless and, therefore, will not be affected by the
gravitational field. If sent in a horizontal direction, it

2 34 The Evolution of Physics

will meet the wall at a point exactly opposite to that at
which it entered.

It seems from this discussion that there is a possibility
of deciding between these two opposite points of view
as the phenomenon would be different for the two ob-
servers. If there is nothing illogical in either of the
explanations just quoted, then our whole previous ar-
gument is destroyed, and we cannot describe all phe-
nomena in two consistent ways, with and without a
gravitational field.

But there is, fortunately, a grave fault in the reason-
ing of the inside observer, which saves our previous
conclusion. He said: A beam of light is weightless
and, therefore, it will not be affected by the gravita-
tional field.” This cannot be right! A beam of light
carries energy and energy has mass. But every inertial
mass is attracted by the gravitational field as inertial
and gravitational masses are equivalent. A beam of light
will bend in a gravitational field exactly as a body
would if thrown horizontally with a velocity equal to
that of light. If the inside observer had reasoned cor-
rectly and had taken into account the bending of light
rays in a gravitational field, then his results would have
been exactly the same as those of an outside observer.

The gravitational field of the earth is, of course, too
weak for the bending of light rays in it to be proved
directly, by experiment. But the famous experiments
performed during the solar eclipses show, conclu-
sively though indirectly, the influence of a gravitational
field on the path of a light ray.

Field, Relativity 235

It follows from these examples that there is a well-
founded hope of formulating a relativistic physics. But
for this we must first tackle the problem of gravitation.

We saw from the example of the elevator the con-
sistency of the two descriptions. Nonuniform motion
may, or may not, be assumed. We can eliminate “abso-
lute” motion from our examples by a gravitational field.
But then there is nothing absolute in the nonuniform
motion. The gravitational field is able to wipe it out
completely.

The ghosts of absolute motion and inertial CS can
be expelled from physics and a new relativistic physics
built. Our idealized experiments show how the prob-
lem of the general relativity theory is closely con-
nected with that of gravitation and why the equiv-
alence of gravitational and inertial mass is so essential
for this connection. It is clear that the solution of the
gravitational problem in the general theory of rela-
tivity must differ from the Newtonian one. The laws
of gravitation must, just as all laws of nature, be formu-
lated for all possible CS, whereas the laws of classical
mechanics, as formulated by Newton, are valid only
in inertial CS.

GEOMETRY AND EXPERIMENT

Our next example will be even more fantastic than
the one with the falling elevator. We have to approach
a new problem; that of a connection between the gen-
eral relativity theory and geometry. Let us begin with
the description of a world in which only two-dimen-

2 3 6 The Evolution of Physics

sional and, not as in ours, three-dimensional creatures
live. The movies have accustomed us to two-dimen-
sional creatures acting on a two-dimensional screen.
Now let us imagine that these shadow figures, that is,
the actors on the screen, really do exist, that they have
the power of thought, that they can create their own
science, that for them a two-dimensional screen stands
for geometrical space. These creatures are unable to
imagine, in a concrete way, a three-dimensional space
just as we are unable to imagine a world of four di-
mensions. They can deflect a straight line; they know
what a circle is, but they are unable to construct a
sphere, because this would mean forsaking their two-
dimensional screen. We are in a similar position. We
are able to deflect and curve lines and surfaces, but we
can scarcely picture a deflected and curved three-
dimensional space.

By living, thinking, and experimenting, our shadow
figures could eventually master the knowledge of the
two-dimensional Euclidean geometry. Thus, they
could prove, for example, that the sum of the angles in
a triangle is 180 degrees. They could construct two
circles with a common center, one very small, the other
large. They would find that the ratio of the circum-
ferences of two such circles is equal to the ratio of
their radii, a result again characteristic of Euclidean
geometry. If the screen were infinitely great, these
shadow beings would find that once having started a
journey straight ahead, they would never return to
their point of departure.

Field, Relativity 237

Let us now imagine these two-dimensional creatures
living in changed conditions. Let us imagine that some-
one from the outside, the “third dimension,” transfers
them from the screen to the surface of a sphere with
a very great radius. If these shadows are very small in
relation to the whole surface, if they have no means of
distant communication and cannot move very far, then
they will not be aware of any change. The sum of
angles in small triangles still amounts to 180 degrees.
Two small circles with a common center still show
that the ratio of their radii and circumferences are
equal. A journey along a straight line never leads them
back to the starting point.

But let these shadow beings, in the course of time,
develop their theoretical and technical knowledge. Let
them find means of communication which will enable
them to cover large distances swiftly. They will then
find that starting on a journey straight ahead, they
ultimately return to their point of departure. “Straight
ahead” means along the great circle of the sphere.
They will also find that the ratio of two circles with a
common center is not equal to the ratio of the radii, if
one of the radii is small and the other great.

If our two-dimensional creatures are conservative, if
they have learned the Euclidean geometry for genera-
tions past when they could not travel far and when
this geometry fitted the facts observed, they will cer-
tainly make every possible effort to hold on to it, de-
spite the evidence of their measurements. They could
try to make physics bear the burden of these discrep-

2 3^ The Evolution of Physics

ancies. They could seek some physical reasons, say
temperature differences, deforming the lines and caus-
ing deviation from Euclidean geometry. But, sooner or
later, they must find out that there is a much more
logical and convincing way of describing these occur-
rences. They will eventually understand that their
world is a finite one, with different geometrical prin-
ciples from those they learned. They will understand
that, in spite of their inability to imagine it, their world
is the two-dimensional surface of a sphere. They will
soon learn new principles of geometry, which though
differing from the Euclidean can, nevertheless, be for-
mulated in an equally consistent and logical way for
their two-dimensional world. For the new generation
brought up with a knowledge of the geometry of the
sphere, the old Euclidean geometry will seem more
complicated and artificial since it does not fit the facts
observed.

Let us return to the three-dimensional creatures of
our world.

What is meant by the statement that our three-
dimensional space has a Euclidean character? The
meaning is that all logically proved statements of the
Euclidean geometry can also be confirmed by actual
experiment. We can, with the help of rigid bodies or
light rays, construct objects corresponding to the
idealized objects of Euclidean geometry. The edge of
a ruler or a light ray corresponds to the line; the sum of
the angles of a triangle built of thin rigid rods is 180
degrees; the ratio of the radii of two circles with a

Field, Relativity 239

common center constructed from thin unbendable wire
is equal to that of their circumferences. Interpreted in
this way, the Euclidean geometry becomes a chapter
of physics, though a very simple one.

But we can imagine that discrepancies have been
discovered, for instance, that the sum of the angles of
a large triangle constructed from rods, which for many
reasons had to be regarded as rigid, is not 180 degrees.
Since we are already used to the idea of the concrete
representation of the objects of Euclidean geometry
by rigid bodies, we should probably seek some physi-
cal force as the cause of such unexpected misbehavior
of our rods. We should try to find the physical nature
of this force and its influence on other phenomena. To
save the Euclidean geometry, we should accuse the ob-
jects of not being rigid, of not exactly corresponding
to those of Euclidean geometry. We should try to find
a better representation of bodies behaving in the way
expected by Euclidean geometry. If, however, we
should not succeed in combining Euclidean geometry
and physics into a simple and consistent picture, we
should have to give up the idea of our space being
Euclidean and seek a more convincing picture of real-
ity under more general assumptions about the geo-
metrical character of our space.

The necessity for this can be illustrated by an ideal-
ized experiment showing that a really relativistic phys-
ics cannot be based upon Euclidean geometry. Our
argument will imply results already learned about iner-
tial CS and the special relativity theory.

24 ° The Evolution of Physics

Imagine a large disk with two circles with a common
center drawn on it, one very small, the other very large.
The disk rotates quickly. The disk is rotating relative
to an outside observer, and there is an inside observer
on the disk. We further assume that the CS of the out-
side observer is an inertial one. The outside observer
may draw, in his inertial CS, the same two circles, small
and large, resting in his CS but coinciding with the
circles on the rotating disk. Euclidean geometry is
valid in his CS since it is inertial, so that he will find the
ratio of the circumferences equal to that of the radii.

But how about the observer on the disk? From the
point of view of classical physics and also the special
relativity theory, his CS is a forbidden one. But if we
intend to find new forms for physical laws, valid in
any CS, then we must treat the observer on the disk

Field, Relativity 241

and the observer outside with equal seriousness. We,
from the outside, are now watching the inside observer
in his attempt to find, by measurement, the circumfer-
ences and radii on the rotating disk. He uses the same
small measuring stick used by the outside observer.
“The same” means either really the same, that is,
handed by the outside observer to the inside, or, one of
two sticks having the same length when at rest in a CS.

The inside observer on the disk begins measuring the
radius and circumference of the small circle. His result
must be the same as that of the outside observer. The
axis on which the disk rotates passes through the cen-
ter. Those parts of the disk near the center have very
small velocities. If the circle is small enough we can
safely apply classical mechanics and ignore the special
relativity theory. This means that the stick has the same
length for the outside and inside observers, and the
result of these two measurements will be the same for
them both. Now the observer on the disk measures the
radius of the large circle. Placed on the radius, the
stick moves, for the outside observer. Such a stick,
however, does not contract and will have the same
length for both observers since the direction of the
motion is perpendicular to the stick. Thus three meas-
urements are the same for both observers: two radii
and the small circumference. But it is not so with the
fourth measurement! The length of the large circum-
ference will be different for the two observers. The
stick placed on the circumference in the direction of
the motion will now appear contracted to the outside

242 The Evolution of Physics

observer, compared to his resting stick. The velocity is
much greater than that of the inner circle, and this
contraction should be taken into account. If, therefore,
we apply the results of the special relativity theory,
our conclusion here is: the length of the great circum-
ference must be different if measured by the two ob-
servers. Since only one of the four lengths measured
by the two observers is not the same for them both,
the ratio of the two radii cannot be equal to the ratio of
the two circumferences for the inside observer as it is
for the outside one. This means that the observer on
the disk cannot confirm the validity of Euclidean ge-
ometry in his CS.

After obtaining this result, the observer on the disk
could say that he does not wish to consider CS in
which Euclidean geometry is not valid. The break-
down of the Euclidean geometry is due to absolute
rotation, to the fact that his CS is a bad and forbidden
one. But, in arguing in this way, he rejects the prin-
cipal idea of the general theory of relativity. On the
other hand, if we wish to reject absolute motion and to
keep up the idea of the general theory of relativity,
then physics must all be built on the basis of a geometry
more general than the Euclidean. There is no way of
escape from this consequence if all CS are permissible.

The changes brought about by the general relativity
theory cannot be confined to space alone. In the spe-
cial relativity theory we had clocks resting in every
CS, having the same rhythm and synchronized, that is,
showing the same time simultaneously. What happens

Field, Relativity 243

to a clock in a noninertial CS? The idealized experi-
ment with the disk will again be of use. The outside
observer has in his inertial CS perfect clocks all having
the same rhythm, all synchronized. The inside observer
takes two clocks of the same kind and places one on
the small inner circle and the other on the large outer
circle. The clock on the inner circle has a very small
velocity relative to the outside observer. We can,
therefore, safely conclude that its rhythm will be the
same as that of the outside clock. But the clock on the
large circle has a considerable velocity, changing its
rhythm compared to the clocks of the outside observer
and, therefore, also compared to the clock placed on
the small circle. Thus, the two rotating clocks will
have different rhythms and, applying the results of the
special relativity theory, we again see that in our rotat-
ing CS we can make no arrangements similar to those
in an inertial CS.

To make clear what conclusions can be drawn from
this and previously described idealized experiments, let
us once more quote a dialogue between the old phys-
icist O, who believes in classical physics, and the mod-
em physicist M, who knows the general relativity
theory. O is the outside observer, in the inertial CS,
whereas M is on the rotating disk.

O. In your CS, Euclidean geometry is not valid. I
watched your measurements and I agree that the ratio
of the two circumferences is not, in your CS, equal to
the ratio of the two radii. But this shows that your CS
is a forbidden one. My CS, however, is of an inertial

244 The Evolution of Physics

character, and I can safely apply Euclidean geometry.
Your disk is in absolute motion and, from the point of
view of classical physics, forms a forbidden CS, in
which the laws of mechanics are not valid.

M. I do not want to hear anything about absolute
motion. My CS is just as good as yours. What I no-
ticed was your rotation relative to my disk. No one
can forbid me to relate all motions to my disk.

O. But did you not feel a strange force trying to
keep you away from the center of the disk? If your
disk were not a rapidly rotating merry-go-round, the
two things which you observed would certainly not
have happened. You would not have noticed the force
pushing you toward the outside nor would you have
noticed that Euclidean geometry is not applicable in
your CS. Are not these facts sufficient to convince you
that your CS is in absolute motion?

M. Not at all! I certainly noticed the two facts you
mention, but I hold a strange gravitational field acting
on my disk responsible for them both. The gravita-
tional field, being directed toward the outside of the
disk, deforms my rigid rods and changes the rhythm of
my clocks. The gravitational field, non-Euclidean ge-
ometry, clocks with different rhythms are, for me, all
closely connected. Accepting any CS, I must at the
same time assume the existence of an appropriate gravi-
tational field with its influence upon rigid rods and
clocks.

O. But are you aware of the difficulties caused by
your general relativity theory? I should like to make

2 45

Field, Relativity

my point clear by taking a simple nonphysical exam-
ple. Imagine an idealized American town consisting of
parallel streets with parallel avenues running perpen-
dicular to them. The distance between the streets and
also between the avenues is always the same. With
these assumptions fulfilled, the blocks are of exactly
the same size. In this way I can easily characterize the
position of any block. But such a construction would
be impossible without Euclidean geometry. Thus, for
instance, we cannot cover our whole earth with one
great ideal American town. One look at the globe will
convince you. But neither could we cover your disk
with such an “American town construction.” You
claim that your rods are deformed by the gravitational
field. The fact that you could not confirm Euclid’s
theorem about the equality of the ratio of radii and
circumferences shows clearly that if you carry such a
construction of streets and avenues far enough you
will, sooner or later, get into difficulties and find that it
is impossible on your disk. Your geometry on your
rotating disk resembles that on a curved surface, where,
of course, the streets-and-avenues construction is im-
possible on a great enough part of the surface. For a
more physical example take a plane irregularly heated
with different temperatures on different parts of the
surface. Can you, with small iron sticks expanding in
length with temperature, carry out the “parallel-per-
pendicular” construction which I have drawn below?
Of course not! Your “gravitational field” plays the,

24 6 The Evolution of Physics

same tricks on your rods as the change of temperature
on the small iron sticks.

M. All this does not frighten me. The street-avenue
construction is needed to determine positions of points,
with the clock to order events. The town need not be
American, it could just as well be ancient European.
Imagine your idealized town made of plasticine and
then deformed. I can still number the blocks and recog-
nize the streets and avenues, though these are no longer

straight and equidistant. Similarly, on our earth, longi-
tude and latitude denote the positions of points, al-
though there is no “American town” construction.

Field, Relativity 247

O. But I still see a difficulty. You are forced to use
your “European town structure.” I agree that you can
order points, or events, but this construction will mud-
dle all measurement of distances. It will not give you
the metric properties of space as does my construction.
Take an example. I know, in my American town, that
to walk ten blocks I have to cover twice the distance
of five blocks. Since I know that all blocks are equal,
I can immediately determine distances.

M. That is true. In my “European town” structure,
I cannot measure distances immediately by the number
of deformed blocks. I must know something more; I
must know the geometrical properties of my surface.
Just as everyone knows that from o° to 10 0 longitude
on the Equator is not the same distance as from o° to
1 o longitude near the North Pole. But every navigator
knows how to judge the distance between two such
points on our earth because he knows its geometrical
properties. He can either do it by calculations based on
the knowledge of spherical trigonometry, or he can do
it experimentally, sailing his ship through the two dis-
tances at the same speed. In your case the whole prob-
lem is trivial, because all the streets and avenues are the
same distance apart. In the case of our earth it is more
complicated; the two meridians o° and io° meet at the
earth’s poles and are furthest apart on the Equator.
Similarly, in my “European town structure,” I must
know something more than you in your “American
town structure,” in order to determine distances. I can
gain this additional knowledge by studying the geo-

248 The Evolution of Physics

metrical properties of my continuum in every particu-
lar case.

O. But all this only goes to show how inconvenient
and complicated it is to give up the simple structure of
the Euclidean geometry for the intricate scaffolding
which you are bound to use. Is this really necessary?

M. I am afraid it is, if we want to apply our physics
to any CS, without the mysterious inertial CS. I agree
that my mathematical tool is more complicated than
yours, but my physical assumptions are simpler and
more natural.

The discussion has been restricted to two-dimen-
sional continua. The point at issue in the general rela-
tivity theory is still more complicated, since it is not
the two-dimensional, but the four-dimensional time-
space continuum. But the ideas are the same as those
sketched in the two-dimensional case. We cannot use
in the general relativity theory the mechanical scaffold-
ing of parallel, perpendicular rods and synchronized
clocks, as in the special relativity theory. In an arbi-
trary CS we cannot determine the point and the instant
at which an event happens by the use of rigid rods,
rhythmical and synchronized clocks, as in the inertial
CS of the special relativity theory. We can still order
the events with our non-Euclidean rods and our clocks
out of rhythm. But actual measurements requiring
rigid rods and perfect rhythmical and synchronized
clocks can be performed only in the local inertial CS.
For this the whole special relativity theory is valid; but
our “good” CS is only local, its inertial character being

Field, Relativity 249

limited in space and time. Even in our arbitrary CS
we can foresee the results of measurements made in
the local inertial CS. But for this we must know the
geometrical character of our time-space continuum.

Our idealized experiments indicate only the general
character of the new relativistic physics. They show us
that our fundamental problem is that of gravitation.
They also show us that the general relativity theory
leads to further generalization of time and space con-
cepts.

GENERAL RELATIVITY AND ITS VERIFICATION

The general theory of relativity attempts to formu-
late physical laws for all CS. The fundamental problem
of the theory is that of gravitation. The theory makes
the first serious effort, since Newton’s time, to re-
formulate the law of gravitation. Is this really neces-
sary? We have already learned about the achievements
of Newton’s theory, about the great development of
astronomy based upon his gravitational law. Newton’s
law still remains the basis of all astronomical calcula-
tions. But we also learned about some objections to the
old theory. Newton’s law is valid only in the inertial
CS of classical physics, in CS defined, we remember,
by the condition that the laws of mechanics must be
valid in them. The force between two masses depends
upon their distance from each other. The connection
between force and distance is, as we know, invariant
with respect to the classical transformation. But this
law does not fit the frame of special relativity. The

250 The Evolution of Physics

distance is not invariant with respect to the Lorentz
transformation. We could try, as we did so success-
fully with the laws of motion, to generalize the gravi-
tational law, to make it fit the special relativity theory,
or, in other words, to formulate it so that it would be
invariant with respect to the Lorentz and not to the
classical transformation. But Newton’s gravitational
law opposed obstinately all our efforts to simplify and
fit it into the scheme of the special relativity theory.
Even if we succeeded in this, a further step would still
be necessary: the step from the inertial CS of the spe-
cial relativity theory to the arbitrary CS of the general
relativity theory. On the other hand, the idealized ex-
periments about the falling elevator show clearly that
there is no chance of formulating the general relativity
theory without solving the problem of gravitation.
From our argument we see why the solution of the
gravitational problem will differ in classical physics
and general relativity.

We have tried to indicate the way leading to the
general relativity theory and the reasons forcing us to
change our old views once more. Without going into
the formal structure of the theory, we shall charac-
terize some features of the new gravitational theory as
compared with the old. It should not be too difficult
to grasp the nature of these differences in view of all
that has previously been said.

1. The gravitational equations of the general rela-
tivity theory can be applied to any CS. It is merely a
matter of convenience to choose any particular CS in

Field, Relativity 2 5 1

a special case. Theoretically all CS are permissible. By
ignoring the gravitation, we automatically come back
to the inertial CS of the special relativity theory.

2. Newton’s gravitational law connects the motion
of a body here and now with the action of a body at
the same time in the far distance. This is the law which
formed a pattern for our whole mechanical view. But
the mechanical view broke down. In Maxwell’s equa-
tions we realized a new pattern for the laws of nature.
Maxwell’s equations are structure laws. They connect
events which happen now and here with events which
will happen a little later in the immediate vicinity.
They are the laws describing the changes of the elec-
tromagnetic field. Our new gravitational equations are
also structure laws describing the changes of the gravi-
tational field. Schematically speaking, we could say:
the transition from Newton’s gravitational law to
general relativity resembles somewhat the transition
from the theory of electric fluids with Coulomb’s law
to Maxwell’s theory.

3. Our world is not Euclidean. The geometrical na-
ture of our world is shaped by masses and their veloci-
ties. The gravitational equations of the general rela-
tivity theory try to disclose the geometrical properties
of our world.

Let us suppose, for the moment, that we have suc-
ceeded in carrying out consistently the program of the
general relativity theory. But are we not in danger of
carrying speculation too far from reality? We know

252 The Evolution of Physics

how well the old theory explains astronomical observa-
tions. Is there a possibility of constructing a bridge
between the new theory and observation? Every specu-
lation must be tested by experiment, and any results,
no matter how attractive, must be rejected if they do
not fit the facts. How did the new theory of gravita-
tion stand the test of experiment? This question can be
answered in one sentence: The old theory is a special
limiting case of the new one. If the gravitational forces
are comparatively weak, the old Newtonian law turns
out to be a good approximation to the new laws of
gravitation. Thus all observations which support the
classical theory also support the general relativity the-
ory. We regain the old theory from the higher level of
the new one.

Even if no additional observation could be quoted in
favor of the new theory, if its explanation were only
just as good as the old one, given a free choice between
the two theories, we should have to decide in favor of
the new one. The equations of the new theory are,
from the formal point of view, more complicated, but
their assumptions are, from the point of view of fun-
damental principles, much simpler. The two frighten-
ing ghosts, absolute time and an inertial system, have
disappeared. The clew of the equivalence of gravita-
tional and inertial mass is not overlooked. No assump-
tion about the gravitational forces and their depend-
ence on distance is needed. The gravitational equations
have the form of structure laws, the form required of

Field, Relativity 253

all physical laws since the great achievements of the
field theory.

Some new deductions, not contained in Newton’s
gravitational law, can be drawn from the new gravita-
tional laws. One, the bending of light rays in a gravita-
tional field, has already been quoted. Two further con-
sequences will now be mentioned.

If the old laws follow from the new one when the
gravitational forces are weak, the deviations from the
Newtonian law of gravitation can be expected only for
comparatively strong gravitational forces. Take our
solar system. The planets, our earth among them, move
along elliptical paths around the sun. Mercury is the
planet nearest the sun. The attraction between the sun
and Mercury is stronger than that between the sun and
any other planet, since the distance is smaller. If there
is any hope of finding a deviation from Newton’s law,
the greatest chance is in the case of Mercury. It fol-
lows, from classical theory, that the path described by
Mercury is of the same kind as that of any other planet
except that it is nearer the sun. According to the gen-
eral relativity theory, the motion should be slightly
different. Not only should Mercury travel around the
sun, but the ellipse which it describes should rotate
very slowly, relative to the CS connected with the
sun. This rotation of the ellipse expresses the new ef-
fect of the general relativity theory. The new theory
predicts the magnitude of this effect. Mercury’s ellipse
would perform a complete rotation in three million
years! We see how small the effect is, and how hope-

254 The Evolution of Physics

less it would be to seek it in the case of planets further
removed from the sun.

The deviation of the motion of the planet Mercury
from the ellipse was known before the general rela-
tivity theory was formulated, and no explanation could
be found. On the other hand, general relativity devel-
oped without any attention to this special problem.
Only later was the conclusion about the rotation of the
ellipse in the motion of a planet around the sun drawn
from the new gravitational equations. In the case of
Mercury, theory explained successfully the deviation
of the motion from the Newtonian law.

But there is still another conclusion which was drawn
from the general relativity theory and compared with
experiment. We have already seen that a clock placed
on the large circle of a rotating disk has a different
rhythm from one placed on the smaller circle. Similarly,
it follows from the theory of relativity that a clock
placed on the sun would have a different rhythm from

Field, Relativity 255

one placed on the earth, since the influence of the
gravitational field is much stronger on the sun than on
the earth.

We remarked on p. 103 that sodium, when incandes-
cent, emits homogeneous yellow light of a definite
wave-length. In this radiation the atom reveals one of
its rhythms, the atom represents, so to speak, a clock
and the emitted wave-length one of its rhythms. Ac-
cording to the general theory of relativity, the wave-
length of light emitted by a sodium atom, say, placed
on the sun should be very slightly greater than that of
light emitted by a sodium atom on our earth.

The problem of testing the consequences of the
general relativity theory by observation is an intricate
one and by no means definitely settled. As we are con-
cerned with principal ideas, we do not intend to go
deeper into this matter, and only state that the verdict
of experiment seems, so far, to confirm the conclusions
drawn from the general relativity theory.

FIELD AND MATTER

We have seen how and why the mechanical point of
view broke down. It was impossible to explain all
phenomena by assuming that simple forces act be-
tween unalterable particles. Our first attempts to go
beyond the mechanical view and to introduce field
concepts proved most successful in the domain of elec-
tromagnetic phenomena. The structure laws for the
electromagnetic field were formulated; laws connect-
ing events very near to each other in space and time.

2 5 6 The Evolution of Physics

These laws fit the frame of the special relativity theory,
since they are invariant with respect to the Lorentz
transformation. Later the general relativity theory for-
mulated the gravitational laws. Again they are struc-
ture laws describing the gravitational field between
material particles. It was also easy to generalize Max-
well’s laws so that they could be applied to any CS,
like the gravitational laws of the general relativity
theory.

We have two realities: matter and field. There is no
doubt that we cannot at present imagine the whole of
physics built upon the concept of matter as the physi-
cists of the early nineteenth century did. For the mo-
ment we accept both the concepts. Can we think of
matter and field as two distinct and different realities?
Given a small particle of matter we could picture in a
naive way that there is a definite surface of the particle
where it ceases to exist and its gravitational field ap-
pears. In our picture, the region in which the laws of
field are valid is abruptly separated from the region in
which matter is present. But what are the physical cri-
terions distinguishing matter and field? Before we
learned about the relativity theory we could have tried
to answer this question in the following way: matter
has mass, whereas field has not. Field represents en-
ergy, matter represents mass. But we already know
that such an answer is insufficient in view of the fur-
ther knowledge gained. From the relativity theory we
know that matter represents vast stores of energy and
that energy represents matter. We cannot, in this way,

Field, Relativity 257

distinguish qualitatively between matter and field,
since the distinction between mass and energy is not a
qualitative one. By far the greatest part of energy is
concentrated in matter; but the field surrounding the
particle also represents energy, though in an incom-
parably smaller quantity. We could therefore say:
Matter is where the concentration of energy is great,
field where the concentration of energy is small. But if
this is the case, then the difference between matter and
field is a quantitative rather than a qualitative one.
There is no sense in regarding matter and field as two
qualities quite different from each other. We cannot
imagine a definite surface separating distinctly field and
matter.

The same difficulty arises for the charge and its field.
It seems impossible to give an obvious qualitative cri-
terion for distinguishing between matter and field or
charge and field.

Our structure laws, that is, Maxwell’s laws and the
gravitational laws, break down for very great concen-
trations of energy or, as we may say, where sources of
the field, that is electric charges or matter, are present.
But could we not slightly modify our equations so that
they would be valid everywhere, even in regions where
energy is enormously concentrated?

We cannot build physics on the basis of the matter-
concept alone. But the division into matter and field is,
after the recognition of the equivalence of mass and
energy, something artificial and not clearly defined.
Could we not reject the concept of matter and build a

258 The Evolution of Physics

pure field physics? What impresses our senses as mat-
ter is really a great concentration of energy into a com-
paratively small space. We could regard matter as the
regions in space where the field is extremely strong. In
this way a new philosophical background could be
created. Its final aim would be the explanation of all
events in nature by structure laws valid always and
everywhere. A thrown stone is, from this point of
view, a changing field, where the states of greatest field
intensity travel through space with the velocity of the
stone. There would be no place, in our new physics,
for both field and matter, field being the only reality.
This new view is suggested by the great achievements
of field physics, by our success in expressing the laws
of electricity, magnetism, gravitation in the form of
structure laws, and finally by the equivalence of mass
and energy. Our ultimate problem would be to modify
our field laws in such a way that they would not break
down for regions in which the energy is enormously
concentrated.

But we have not so far succeeded in fulfilling this
program convincingly and consistently. The deci-
sion, as to whether it is possible to carry it out, belongs
to the future. At present we must still assume in all
our actual theoretical constructions two realities: field
and matter.

Fundamental problems are still before us. We know
that all matter is constructed from a few kinds of par-
ticles only. How are the various forms of matter built
from these elementary particles? How do these ele-

Field, Relativity 2 59

mentary particles interact with the field? By the search
for an answer to these questions new ideas have been
introduced into physics, the ideas of the quantum
theory.

We Summarize:

A new concept appears in physics, the most important
invention since Newton's time: the field. It needed great
scientific imagination to realize that it is not the charges
nor the particles but the field in the space between the
charges and the particles which is essential for the descrip-
tion of physical phenomena. The field concept proves most
successful and leads to the formulation of Maxwell's equa-
tions describing the structure of the electromagnetic field
and governing the electric as well as the optical phe-
nomena.

The theory of relativity arises from the field problems.
The contradictions and inconsistencies of the old theories
force us to ascribe new properties to the time-space con-
tinuum, to the scene of all events in our physical world.

The relativity theory develops in two steps. The first
step leads to what is known as the special theory of rela-
tivity , applied only to inertial co-ordinate systems, that is,
to systems in which the law of inertia, as forrmdated by
Newton, is valid. T he special theory of relativity is based
on two fundamental assumptions: physical laws are the
same in all co-ordinate systems moving uniformly , rela-
tive to each other; the velocity of light always has the
same value. From these assumptions, fully confirmed by
experiment, the properties of moving rods and clocks,
their changes in length and rhythm depending on velocity,
are deduced. The theory of relativity changes the laws of
mechanics. The old laws are invalid if the velocity of the
moving particle approaches that of light. The new laws
for a moving body as reformulated by the relativity the-

260 The Evolution of Physics

ory are splendidly confirmed by experiment. A further
consequence of the (special) theory of relativity is the
connection between mass and energy. Mass is energy and
energy has mass. The two conservation laws of mass and
energy are combined by the relativity theory into one, the
conservation law of mass-energy .

The general theory of relativity gives a still deeper anal-
ysis of the time-space continuum. The validity of the
theory is no longer restricted to inertial co-ordinate sys-
tems. The theory attacks the problem of gravitation and
formulates new structure laws for the gravitational field.
It forces us to analyze the role played by geometry in the
description of the physical world. It regards the fact that
gravitational and inertial mass are equal, as essential and
not merely accidental, as in classical mechanics. The ex-
perimental consequences of the general relativity theory
differ only slightly from those of classical mechanics. They
stand the test of experiment well wherever comparison is
possible. But the strength of the theory lies in its inner
consistency and the simplicity of its fundamental assump-
tions.

The theory of relativity stresses the importance of the
field concept in physics. But we have not yet succeeded in
formulating a pure field physics. For the present we must
still assume the existence of both: field and matter.

IV. QUANTA

Quanta

Continuity— discontinuity . . . Elementary quanta of mat-
ter and electricity .. .The quanta of light . . . Light spectra
• . .The waves of matter . . . Probability waves . . . Physics
and reality

CONTINUITY— DISCONTINUITY

A map of New York City and the surrounding coun-
try is spread before us. We ask: which points on this
map can be reached by train? After looking up these
points in a railway timetable, we mark them on the
map. We now change our question and ask: which
points can be reached by car? If we draw lines on the
map representing all the roads starting from New York,
every point on these roads can, in fact, be reached by
car. In both cases we have sets of points. In the first
they are separated from each other and represent the
different railway stations, and in the second they are
the points along the lines representing the roads. Our
next question is about the distance of each of these
points from New York, or, to be more rigorous, from
a certain spot in that city. In the first case, certain
numbers correspond to the points on our map. These
numbers change by irregular, but always finite, leaps
and bounds. We say: the distances from New York
of the places which can be reached by train change
only in a discontinuous way. Those of the places which

263

264 The Evolution of Physics

can be reached by car, however, may change by steps
as small as we wish, they can vary in a continuous way.
The changes in distance can be made arbitrarily small
in the case of a car, but not in the case of a train.

The output of a coal mine can change in a continu-
ous way. The amount of coal produced can be de-
creased or increased by arbitrarily small steps. But the
number of miners employed can change only discon-
tinuously. It would be pure nonsense to say: “Since
yesterday, the number of employees has increased by
3 . 783 -”

Asked about the amount of money in his pocket, a
man can give a number containing only two decimals.
A sum of money can change only by jumps, in a dis-
continuous way. In America the smallest permissible
change or, as we shall call it, the “elementary quantum”
for American money, is one cent. The elementary
quantum for English money is one farthing, worth
only half the American elementary quantum. Here we
have an example of two elementary quanta whose mu-
tual values can be compared. The ratio of their values
has a definite sense since one of them is worth twice as
much as the other.

We can say: some quantities can change continu-
ously and others can change only discontinuously, by
steps which cannot be further decreased. These indi-
visible steps are called the elementary quanta of the
particular quantity to which they refer.

We can weigh large quantities of sand and regard its
mass as continuous even though its granular structure

Quanta 265

is evident. But if the sand were to become very precious
and the scales used very sensitive, we should have to
consider the fact that the mass always changes by a
multiple number of one grain. The mass of this one
grain would be our elementary quantum. From this ex-
ample we see how the discontinuous character of a
quantity, so far regarded as continuous, can be detected
by increasing the precision of our measurements.

If we had to characterize the principal idea of the
quantum theory in one sentence, we could say: it must
be assumed that some physical quantities so jar re-
garded as continuous are composed of elementary
quanta.

The region of facts covered by the quantum theory
is tremendously great. These facts have been disclosed
by the highly developed technique of modem experi-
ment. As we can neither show nor describe even the
basic experiments, we shall frequently have to quote
their results dogmatically. Our aim is to explain the
principal underlying ideas only.

ELEMENTARY QUANTA OF MATTER AND ELECTRICITY

In the picture of matter drawn by the kinetic the-
ory, all elements are built of molecules. Take the sim-
plest case of the lightest element, that is hydrogen. On
p. 67 we saw how the study of Brownian motions led
to the determination of the mass of one hydrogen
molecule. Its value is:

0.000 000 000 000 000 000 000 003 3 grams.

266

The Evolution of Physics

This means that mass is discontinuous. The mass of a
portion of hydrogen can change only by a whole num-
ber of small steps each corresponding to the mass of
one hydrogen molecule. But chemical processes show
that the hydrogen molecule can be broken up into two
parts, or, in other words, that the hydrogen molecule
is composed of two atoms. In chemical processes it is
the atom and not the molecule which plays the role of
an elementary quantum. Dividing the above number
by two, we find the mass of a hydrogen atom. This is
about

o.ooo ooo ooo ooo ooo ooo ooo 0017 grains.

Mass is a discontinuous quantity. But, of course, we
need not bother about this when determining weight.
Even the most sensitive scales are far from attaining the
degree of precision by which the discontinuity in mass
variation could be detected.

Let us return to a well-known fact. A wire is con-
nected with the source of a current. The current is
flowing through the wire from higher to lower poten-
tial. We remember that many experimental facts were
explained by the simple theory of electric fluids flow-
ing through the wire. We also remember (p. 82) that
the decision as to whether the positive fluid flows from
higher to lower potential, or the negative fluid flows
from lower to higher potential, was merely a matter of
convention. For the moment we disregard all the fur-
ther progress resulting from the field concepts. Even
when thinking in the simple terms of electric fluids,

Quanta 167

there still remain some questions to be settled. As the
name “fluid” suggests, electricity was regarded, in the
early days, as a continuous quantity. The amount of
charge could be changed, according to these old views,
by arbitrarily small steps. There was no need to assume
elementary electric quanta. The achievements of the
kinetic theory of matter prepared us for a new ques-
tion: do elementary quanta of electric fluids exist? The
other question to be settled is: does the current consist
of a flow of positive, negative or perhaps of both
fluids?

The idea of all the experiments answering these
questions is to tear the electric fluid from the wire, to
let it travel through empty space, to deprive it of any
association with matter and then to investigate its prop-
erties, which must appear most clearly under these con-
ditions. Many experiments of this kind were performed
in the late nineteenth century. Before explaining the
idea of these experimental arrangements, at least in one
case, we shall quote the results. The electric fluid flow-
ing through the wire is a negative one, directed, there-
fore, from lower to higher potential. Had we known
this from the start, when the theory of electric fluids
was first formed, we should certainly have inter-
changed the words, and called the electricity of the
rubber rod positive, that of the glass rod negative. It
would then have been more convenient to regard the
flowing fluid as the positive one. Since our first guess
was wrong we now have to put up with the incon-
venience. The next important question is whether the

268 The Evolution of Physics

structure of this negative fluid is “granular,” whether
or not it is composed of electric quanta. Again a num-
ber of independent experiments show that there is no
doubt as to the existence of an elementary quantum of
this negative electricity. The negative electric fluid is
constructed of grains, just as the beach is composed of
grains of sand, or a house built of bricks. This result
was formulated most clearly by J. J. Thomson, about
forty years ago. The elementary quanta of negative
electricity are called electrons. Thus every negative
electric charge is composed of a multitude of elemen-
tary charges represented by electrons. The negative
charge can, like mass, vary only discontinuously. The
elementary electric charge is, however, so small that in
many investigations it is equally possible and some-
times even more convenient to regard it as a continu-
ous quantity. Thus the atomic and electron theories
introduce into science discontinuous physical quanti-
ties which can vary only by jumps.

Imagine two parallel metal plates in some place from
which all air has been extracted. One of the plates has
a positive, the other a negative charge. A positive test
charge brought between the two plates will be repelled
by the positively charged and attracted by the nega-
tively charged plate. Thus the lines of force of the
electric field will be directed from the positively to
the negatively charged plate. A force acting on a nega-
tively charged test body would have the opposite di-
rection. If the plates are sufficiently large, the lines of
force between them will be equally dense everywhere;

Quanta

269

it is immaterial where the test body is placed, the force
and, therefore, the density of the lines of force will be

the same. Electrons brought somewhere between the
plates would behave like raindrops in the gravitational
field of the earth, moving parallel to each other from
the negatively to the positively charged plate. There
are many known experimental arrangements for bring-
ing a shower of electrons into such a field which di-
rects them all in the same way. One of the simplest is
to bring a heated wire between the charged plates.
Such a heated wire emits electrons which are after-
wards directed by the lines of force of the external
field. For instance, radio tubes, familiar to everyone,
are based on this principle.

Many very ingenious experiments have been per-
formed on a beam of electrons. The changes of their
path in different electric and magnetic external fields
have been investigated. It has even been possible to iso-
late a single electron and to determine its elementary
charge and its mass, that is, its inertial resistance to the

270 The Evolution of Physics

action of an external force. Here we shall only quote
the value of the mass of an electron. It turned out to
be about two thousand times smaller than the mass of
a hydrogen atom. Thus the mass of a hydrogen atom,
small as it is, appears great in comparison with the mass
of an electron. From the point of view of a consistent
field theory, the whole mass, that is, the whole energy,
of an electron is the energy of its field; the bulk of its
strength is within a very small sphere, and away from
the “center” of the electron it is weak.

We said before that the atom of any element is its
smallest elementary quantum. This statement was be-
lieved for a very long time. Now, however, it is no
longer believed! Science has formed a new view show-
ing the limitations of the old one. There is scarcely
any statement in physics more firmly founded on facts
than the one about the complex structure of the atom.
First came the realization that the electron, the elemen-
tary quantum of the negative electric fluid, is also one
of the components of the atom, one of the elementary
bricks from which all matter is built. The previously
quoted example of a heated wire emitting electrons is
only one of the numerous instances of the extraction
of these particles from matter. This result closely con-
necting the problem of the structure of matter with
that of electricity follows, beyond any doubt, from
very many independent experimental facts.

It is comparatively easy to extract from an atom
some of the electrons from which it is composed. This
can be done by heat, as in our example of a heated

Quanta 271

wire, or in a different way, such as by bombarding
atoms with other electrons.

Suppose a thin, red-hot, metal wire is inserted into
rarefied hydrogen. The wire will emit electrons in all
directions. Under the action of a foreign electric field
a given velocity will be imparted to them. An electron
increases its velocity just as a stone falling in the gravi-
tational field. By this method we can obtain a beam
of electrons rushing along with a definite speed in a
definite direction. Nowadays, we can reach velocities
comparable to that of light by submitting electrons to
the action of very strong fields. What happens, then,
when a beam of electrons of a definite velocity im-
pinges on the molecules of rarefied hydrogen? The
impact of a sufficiently speedy electron will not only
disrupt the hydrogen molecule into its two atoms but
will also extract an electron from one of the atoms.

Let us accept the fact that electrons are constituents
of matter. Then, an atom from which an electron has
been torn out cannot be electrically neutral. If it was
previously neutral, then it cannot be so now, since it is
poorer by one elementary charge. That which remains
must have a positive charge. Furthermore, since the
mass of an electron is so much smaller than that of the
lightest atom, we can safely conclude that by far the
greater part of the mass of the atom is not represented
by electrons but by the remainder of the elementary
particles which are much heavier than the electrons.
We call this heavy part of the atom its nucleus.

Modem experimental physics has developed meth-

272 The Evolution of Physics

ods of breaking up the nucleus of the atom, of chang-
ing atoms of one element into those of another, and of
extracting from the nucleus the heavy elementary par-
ticles of which it is built. This chapter of physics,
known as “nuclear physics,” to which Rutherford
contributed so much, is, from the experimental point
of view, the most interesting. But a theory, simple in
its fundamental ideas and connecting the rich variety
of facts in the domain of nuclear physics, is still lack-
ing. Since, in these pages, we are interested only in
general physical ideas, we shall omit this chapter in
spite of its great importance in modern physics.

THE QUANTA OF LIGHT

Let us consider a wall built along the seashore. The
waves from the sea continually impinge on the wall,
wash away some of its surface, and retreat, leaving the
way clear for the incoming waves. The mass of the
wall decreases and we can ask how much is washed
away in, say, one year. But now let us picture a differ-
ent process. We want to diminish the mass of the wall
by the same amount as previously but in a different
way. We shoot at the wall and split it at the places
where the bullets hit. The mass of the wall will be
decreased and we can well imagine that the same re-
duction in mass is achieved in both cases. But from the
appearance of the wall we could easily detect whether
the continuous sea wave or the discontinuous shower
of bullets has been acting. It will be helpful in under-
standing the phenomena which we are about to de-

Quanta 275

scribe, to bear in mind the difference between sea
waves and a shower of bullets.

We said, previously, that a heated wire emits elec-
trons. Mere we shall introduce another way of extract-
ing electrons from metal. Homogeneous light, such as
violet light, which is, as we know, light of a definite
wave-length, is impinging on a metal surface. The
light extracts electrons from the metal. The electrons
are torn from the metal and a shower of them speeds
along with a certain velocity. From the point of view
of the energy principle we can say: the energy of light
is partially transformed into the kinetic energy of ex-
pelled electrons. Modern experimental technique en-
ables us to register these electron-bullets, to determine
their velocity and thus their energy. This extraction
of electrons by light falling upon metal is called the
photoelectric effect.

Our starting point was the action of a homogeneous
light wave, with some definite intensity. As in every
experiment, we must now change our arrangements to
see whether this will have any influence on the ob-
served effect.

Let us begin by changing the intensity of the homo-
geneous violet light falling on the metal plate and note
to what extent the energy of the emitted electrons de-
pends upon the intensity of the light. Let us try to find
the answer by reasoning instead of by experiment. We
could argue: in the photoelectric effect a certain defi-
nite portion of the energy of radiation is transformed
into energy of motion of the electrons. If we again il-

274 Evolution of Physics

luminate the metal with light of the same wave-length
but from a more powerful source, then the energy of
the emitted electrons should be greater, since the radia-
tion is richer in energy. We should, therefore, expect
the velocity of the emitted electrons to increase if the
intensity of the light increases. But experiment again
contradicts our prediction. Once more we see that the
laws of nature are not as we should like them to be.
We have come upon one of the experiments which,
contradicting our predictions, breaks the theory on
which they were based. The actual experimental result
is, from the point of view of the wave theory, aston-
ishing. The observed electrons all have the same speed,
the same energy, which does not change when the in-
tensity of the light is increased.

This experimental result could not be predicted by
the wave theory. Here again a new theory arises from
the conflict between the old theory and experiment.

Let us be deliberately unjust to the wave theory of
light, forgetting its great achievements, its splendid ex-
planation of the bending of light around very small
obstacles. With our attention focused on the photo-
electric effect, let us demand from the theory an ade-
quate explanation of this effect. Obviously, we cannot
deduce from the wave theory the independence of the
energy of electrons from the intensity of light by
which they have been extracted from the metal plate.
We shall, therefore, try another theory. We remem-
ber that Newton’s corpuscular theory, explaining many
of the observed phenomena of light, failed to account

Quanta 275

for the bending of light, which we are now deliberately
disregarding. In Newton’s time the concept of energy
did not exist. Light corpuscles were, according to him,
weightless; each color preserved its own substance
character. Later, when the concept of energy was
created and it was recognized that light carries energy,
no one thought of applying these concepts to the cor-
puscular theory of light. Newton’s theory was dead
and, until our own century, its revival was not taken
seriously.

To keep the principal idea of Newton’s theory, we
must assume that homogeneous light is composed of
energy-grains and replace the old light corpuscles by
light quanta, which we shall call photons , small por-
tions of energy, traveling through empty space with
the velocity of light. The revival of Newton’s theory
in this new form leads to the quantum theory of light.
Not only matter and electric charge, but also energy of
radiation has a granular structure, i.e., is built up of
light quanta. In addition to quanta of matter and quanta
of electricity there are also quanta of energy.

The idea of energy quanta was first introduced by
Planck at the beginning of this century in order to ex-
plain some effects much more complicated than the
photoelectric effect. But the photo-effect shows most
clearly and simply the necessity for changing our old
concepts.

It is at once evident that this quantum theory of
light explains the photoelectric effect. A shower of
photons is falling on a metal plate. The action between

27 6 The Evolution of Physics

radiation and matter consists here of very many single
processes in which a photon impinges on the atom and
tears out an electron. These single processes are all
alike and the extracted electron will have the same
energy in every case. We also understand that increas-
ing the intensity of the light means, in our new lan-
guage, increasing the number of falling photons. In
this case, a different number of electrons would be
thrown out of the metal plate, but the energy of any
single one would not change. Thus we see that this
theory is in perfect agreement with observation.

What will happen if a beam of homogeneous light
of a different color, say, red instead of violet, falls on
the metal surface? Let us leave experiment to answer
this question. The energy of the extracted electrons
must be measured and compared with the energy of
electrons thrown out by violet light. The energy of
the electron extracted by red light turns out to be
smaller than the energy of the electron extracted by
violet light. This means that the energy of the light
quanta is different for different colors. The photons
belonging to the color red have half the energy of
those belonging to the color violet. Or, more rigor-
ously: the energy of a light quantum belonging to a
homogeneous color decreases proportionally as the
wave-length increases. There is an essential difference
between quanta of energy and quanta of electricity.
Light quanta differ for every wave-length, whereas
quanta of electricity are always the same. If we were
to use one of our previous analogies, we should com-

Quanta 277

pare light quanta to the smallest monetary quanta, dif-
fering in each country.

Let us continue to discard the wave theory of light
and assume that the structure of light is granular and
is formed by light quanta, that is, photons speeding
through space with the velocity of light. Thus, in our
new picture, light is a shower of photons, and the
photon is the elementary quantum of light energy. If,
however, the wave theory is discarded, the concept of
a wave-length disappears. What new concept takes its
place? The energy of the light quanta! Statements ex-
pressed in the terminology of the wave theory can be
translated into statements of the quantum theory of
radiation. For example:

Terminology of the
Wave Theory

Homogeneous light has a
definite wave-length. The
wave-length of the red end
of the spectrum is twice
that of the violet end.

Terminology of the
Quantum Theory

Homogeneous light con-
tains photons of a definite
energy. The energy of the
photon for the red end of
the spectrum is half that of
the violet end.

The state of affairs can be summarized in the fol-
lowing way: there are phenomena which can be ex-
plained by the quantum theory but not by the wave
theory. Photo-effect furnishes an example, though
other phenomena of this kind are known. There are
phenomena which can be explained by the wave theory
but not by the quantum theory. The bending of light
around obstacles is a typical example. Finally, there

278 The Evolution of Physics

are phenomena, such as the rectilinear propagation of
light, which can be equally well explained by the
quantum and the wave theory of light.

But what is light really? Is it a wave or a shower of
photons? Once before we put a similar question when
we asked: is light a wave or a shower of light cor-
puscles? At that time there was every reason for dis-
carding the corpuscular theory of light and accepting
the wave theory, which covered all phenomena. Now,
however, the problem is much more complicated.
There seems no likelihood of forming a consistent de-
scription of the phenomena of light by a choice of only
one of the two possible languages. It seems as though
we must use sometimes the one theory and sometimes
the other, while at times we may use either. We are
faced with a new kind of difficulty. We have two con-
tradictory pictures of reality; separately neither of
them fully explains the phenomena of light, but to-
gether they do!

How is it possible to combine these two pictures?
How can we understand these two utterly different
aspects of light? It is not easy to account for this new
difficulty. Again we are faced with a fundamental
problem.

For the moment let us accept the photon theory of
light and try, by its help, to understand the facts so
far explained by the wave theory. In this way we shall
stress the difficulties which make the two theories ap-
pear, at first sight, irreconcilable.

We remember: a beam of homogeneous light pass-

Quanta 279

ing through a pinhole gives light and dark rings (p.
1 18). How is it possible to understand this phenomena
by the help of the quantum theory of light, disregard-
ing the wave theory? A photon passes through the
hole. We could expect the screen to appear light if the
photon passes through and dark if it does not. Instead,
we find light and dark rings. We could try to account
for it as follows: perhaps there is some interaction be-
tween the rim of the hole and the photon which is
responsible for the appearance of the diffraction rings.
This sentence can, of course, hardly be regarded as an
explanation. At best, it outlines a program for an ex-
planation holding out at least some hope of a future
understanding of diffraction by interaction between
matter and photons.

But even this feeble hope is dashed by our previous
discussion of another experimental arrangement. Let
us take two pinholes. Homogeneous light passing
through the two holes gives light and dark stripes on
the screen. How is this effect to be understood from
the point of view of the quantum theory of light? We
could argue: a photon passes through either one of the
two pinholes. If a photon of homogeneous light repre-
sents an elementary light particle, we can hardly imag-
ine its division and its passage through the two holes.
But then the effect should be exactly as in the first
case, fight and dark rings and not fight and dark
stripes. How is it possible then that the presence of an-
other pinhole completely changes the effect? Appar-
ently the hole through which the photon does not pass.

28 o

The Evolution of Physics

even though it may be at a fair distance, changes the
rings into stripes! If the photon behaves like a cor-
puscle in classical physics it must pass through one of
the two holes. But in this case, the phenomena of dif-
fraction seem quite incomprehensible.

Science forces us to create new ideas, new theories.
Their aim is to break down the wall of contradictions
which frequently blocks the way of scientific progress.
All the essential ideas in science were born in a dramatic
conflict between reality and our attempts at under-
standing. Here again is a problem for the solution of
which new principles are needed. Before we try to ac-
count for the attempts of modern physics to explain
the contradiction between the quantum and the wave
aspects of light, we shall show that exactly the same
difficulty appears when dealing with quanta of matter
instead of quanta of light.

LIGHT SPECTRA

We already know that all matter is built of only a
few kinds of particles. Electrons were the first elemen-
tary particles of matter to be discovered. But electrons
are also the elementary quanta of negative electricity.
We learned furthermore that some phenomena force
us to assume that light is composed of elementary light
quanta, differing for different wave-lengths. Before
proceeding we must discuss some physical phenomena
in which matter as well as radiation plays an essential
role.

The sun emits radiation which can be split into its

Quanta 281

components by a prism. The continuous spectrum of
the sun can thus be obtained. Every wave-length be-
tween the two ends of the visible spectrum is repre-
sented. Let us take another example. It was previously
mentioned that sodium when incandescent emits ho-
mogeneous light, light of one color or one wave-length.
If incandescent sodium is placed before the prism we
see only one yellow line. In general, if a radiating body
is placed before the prism, then the light it emits is split
up into its components, revealing the spectrum charac-
teristic of the emitting body.

The discharge of electricity in a tube containing gas
produces a source of light such as seen in the neon
tubes used for luminous advertisements. Suppose such
a tube is placed before a spectroscope. The spectro-
scope is an instrument which acts like a prism, but with
much greater accuracy and sensitiveness; it splits light
into its components, that is, it analyzes it. Light from
the sun, seen through a spectroscope, gives a continu-
ous spectrum; all wave-lengths are represented in it. If,
however, the source of light is a gas through which a
current of electricity passes, the spectrum is of a differ-
ent character. Instead of the continuous, multi-colored
design of the sun’s spectrum, bright, separated stripes
appear on a continuous dark background. Every stripe,
if it is very narrow, corresponds to a definite color or,
in the language of the wave theory, to a definite wave-
length. For example, if twenty lines are visible in the
spectrum, each of them will be designated by one of
twenty numbers expressing the corresponding wave-

282 The Evolution of Physics

length. The vapors of the various elements possess dif-
ferent systems of lines, and thus different combinations
of numbers designating the wave-lengths composing
the emitted light spectrum. No two elements have
identical systems of stripes in their characteristic spec-
tra, just as no two persons have exactly identical finger-
prints. As a catalogue of these lines was worked out
by physicists, the existence of laws gradually became
evident, and it was possible to replace some of the
columns of seemingly disconnected numbers express-
ing the length of the various waves by one simple
mathematical formula.

All that has just been said can now be translated into
the photon language. The stripes correspond to certain
definite wave-lengths or, in other words, to photons
with a definite energy. Luminous gases do not, there-
fore, emit photons with all possible energies, but only
those characteristic of the substance. Reality again lim-
its the wealth of possibilities.

Atoms of a particular element, say, hydrogen, can
emit only photons with definite energies. Only the
emission of definite energy quanta is permissible, all
others being prohibited. Imagine, for the sake of sim-
plicity, that some element emits only one line, that is,
photons of a quite definite energy. The atom is richer
in energy before the emission and poorer afterwards.
From the energy principle it must follow that the
energy level of an atom is higher before emission and
lower afterwards, and that the difference between the

Quanta 283

two levels must be equal to the energy of the emitted
photon. Thus the fact that an atom of a certain ele-
ment emits radiation of one wave-length only, that is
photons of a definite energy only, could be expressed
differently: only two energy levels are permissible in
an atom of this element and the emission of a photon
corresponds to the transition of the atom from the
higher to the lower energy level.

But more than one line appears in the spectra of the
elements, as a rule. The photons emitted correspond to
many energies and not to one only. Or, in other words,
we must assume that many energy levels are allowed in
an atom and that the emission of a photon corresponds
to the transition of the atom from a higher energy level
to a lower one. But it is essential that not every energy
level should be permitted, since not every wave-length,
not every photon-energy, appears in the spectra of an
element. Instead of saying that some definite lines,
some definite wave-lengths, belong to the spectrum of
every atom, we can say that every atom has some defi-
nite energy levels, and that the emission of light quanta
is associated with the transition of the atom from one
energy level to another. The energy levels are, as a
rule, not continuous but discontinuous. Again we see
that the possibilities are restricted by reality.

It was Bohr who showed for the first time why just
these and no other lines appear in the spectra. His
theory, formulated twenty-five years ago, draws a pic-
ture of the atom from which, at any rate in simple

2 84 The Evolution of Physics

cases, the spectra of the elements can be calculated and
the apparently dull and unrelated numbers are sud-
denly made coherent in the light of the theory.

Bohr’s theory forms an intermediate step toward a
deeper and more general theory, called the wave or
quantum mechanics. It is our aim in these last pages to
characterize the principal ideas of this theory. Before
doing so, we must mention one more theoretical and
experimental result of a more special character.

Our visible spectrum begins with a certain wave-
length for the violet color and ends with a certain
wave-length for the red color. Or, in other words, the
energies of the photons in the visible spectrum are al-
ways enclosed within the limits formed by the photon
energies of the violet and red lights. This limitation is,
of course, only a property of the human eye. If the dif-
ference in energy of some of the energy levels is suffi-
ciently great, then an ultraviolet photon will be sent
out, giving a line beyond the visible spectrum. Its pres-
ence cannot be detected by the naked eye; a photo-
graohic plate must be used.

X rays are also composed of photons of a much
greater energy than those of visible light, or in other
words, their wave-lengths are much smaller, thousands
of times smaller in fact, than those of visible light.

But is it possible to determine such small wave-
lengths experimentally? It was difficult enough to do so
for ordinary light. We had to have small obstacles or
small apertures. Two pinholes very near to each other,

Quanta 285

showing diffraction for ordinary light, would have to
be many thousands of times smaller and closer together
to show diffraction for X rays.

How then can we measure the wave-lengths of these
rays? Nature herself comes to our aid.

A crystal is a conglomeration of atoms arranged at
very short distances from each other on a perfectly
regular plan. Our drawing shows a simple model of the

structure of a crystal. Instead of minute apertures,
there are extremely small obstacles formed by the
atoms of the element, arranged very close to each other
in absolutely regular order. The distances between the
atoms, as found from the theory of the crystal struc-
ture, are so small that they might be expected to show
the effect of diffraction for X rays. Experiment proved
that it is, in fact, possible to diffract the X-ray wave by
means of these closely packed obstacles disposed in the

286 The Evolution of Physics

regular three-dimensional arrangement occurring in a
crystal.

Suppose that a beam of X rays falls upon a crystal
and, after passing through it, is recorded on a photo-
graphic plate. The plate then shows the diffraction pat-
tern. Various methods have been used to study the
X-ray spectra, to deduce data concerning the wave-
length from the diffraction pattern. What has been
said here in a few words would fill volumes if all the-
oretical and experimental details were set forth. In
Plate III we give only one diffraction pattern obtained
by one of the various methods. We again see the dark
and light rings so characteristic of the wave theory. In
the center the non-diffracted ray is visible. If the crys-
tal were not brought between the X rays and the pho-
tographic plate, only the light spot in the center would
be seen. From photographs of this kind the wave-
lengths of the X-ray spectra can be calculated and, on
the other hand, if the wave-length is known, conclu-
sions can be drawn about the structure of the crystal.

THE WAVES OF MATTER

How can we understand the fact that only certain
characteristic wave-lengths appear in the spectra of the
elements?

It has often happened in physics that an essential
advance was achieved by carrying out a consistent
analogy between apparently unrelated phenomena. In
these pages we have often seen how ideas created and

PLATE III

Spectral lines.

( Photographed by Lastoiviecki and Gregor)
Diffraction of X rays.

( Photographed by Loria and Klinger )
Diffraction of electronic waves.

Quanta 287

developed in one branch of science were afterwards
successfully applied to another. The development of
the mechanical and field views gives many examples of
this kind. The association of solved problems with
those unsolved may throw new light on our difficulties
by suggesting new ideas. It is easy to find a superficial
analogy which really expresses nothing. But to dis-
cover some essential common features, hidden beneath
a surface of external differences, to form, on this basis,
a new successful theory, is important creative work.
The development of the so-called wave mechanics,
begun by de Broglie and Schrodinger, less than fifteen
years ago, is a typical example of the achievement of a
successful theory by means of a deep and fortunate
analogy.

Our starting point is a classical example having
nothing to do with modem physics. We take in our
hand the end of a very long flexible rubber tube, or a
very long spring, and try to move it rhythmically up
and down, so that the end oscillates. Then, as we have
seen in many other examples, a wave is created by the
oscillation which spreads through the tube with a cer-

tain velocity. If we imagine an infinitely long tube,
then the portions of waves, once started, will pursue
their endless journey without interference.

Now another case. The two ends of the same tube

288

The Evolution of Physics

are fastened. If preferred, a violin string may be used.
What happens now if a wave is created at one end of
the rubber tube or cord? The wave begins its journey
as in the previous example, but it is soon reflected by
the other end of the tube. We now have two waves:
one created by oscillation, the other by reflection; they
travel in opposite directions and interfere with each
other. It would not be difficult to trace the interference
of the two waves and discover the one wave resulting
from their superposition; it is called the standing wave.
The two words “standing” and “wave” seem to con-
tradict each other; their combination is, nevertheless,
justified by the result of the superposition of the two

waves.

The simplest example of a standing wave is the mo-
tion of a cord with the two ends fixed, an up-and-down
motion, as shown in our drawing. This motion is the

result of one wave lying on the other when the two are
traveling in opposite directions. The characteristic fea-
ture of this motion is: only the two end points are at
rest. They are called nodes. The wave stands, so to
speak, between the two nodes, all points of the cord

Quanta 289

reaching simultaneously the maxima and minima of
their deviation.

But this is only the simplest kind of a standing wave.
There are others. For example, a standing wave can
have three nodes, one at each end and one in the center.
In this case three points are always at rest. A glance at

h

the drawings shows that here the wave-length is half
as great as the one with two nodes. Similarly, standing
waves can have four, five, and more nodes. The wave-
length in each case will depend on the number of

nodes. This number can only be an integer and can
change only by jumps. The sentence, “the number of
nodes in a standing wave is 3.576,” is pure nonsense.
Thus the wave-length can only change discontinu-
ously. Here, in this most classical problem, we recog-
nize the familiar features of the quantum theory. The
standing wave produced by a violin player is, in fact,
still more complicated, being a mixture of very many
waves with two, three, four, five, and more nodes and,
therefore, a mixture of several wave-lengths. Physics
can analyze such a mixture into the simple standing

290 The Evolution of Physics

waves from which it is composed. Or, using our previ-
ous terminology, we could say that the oscillating
string has its spectrum, just as an element emitting
radiation. And, in the same way as for the spectrum of
an element, only certain wave-lengths are allowed, all
others being prohibited.

We have thus discovered some similarity between
the oscillating cord and the atom emitting radiation.
Strange as this analogy may seem, let us draw further
conclusions from it and try to proceed with the com-
parison, once having chosen it. The atoms of every ele-
ment are composed of elementary particles, the heavier
constituting the nucleus, and the lighter the electrons.
Such a system of particles behaves like a small acous-
tical instrument in which standing waves are produced.

Yet the standing wave is the result of interference
between two or, generally, even more moving waves.
If there is some truth in our analogy, a still simpler ar-
rangement than that of the atom should correspond to
a spreading wave. What is the simplest arrangement?
In our material world, nothing can be simpler than an
electron, an elementary particle, on which no forces
are acting, that is, an electron at rest or in uniform mo-
tion. We could guess a further link in the chain of our
analogy: electron moving uniformly -> waves of a
definite length. This was de Broglie’s new and coura-
geous idea.

It was previously shown that there are phenomena in
which light reveals its wave-like character and others
in which light reveals its corpuscular character. After

Quanta 291

becoming used to the idea that light is a wave, we
found, to our astonishment, that in some cases, for in-
stance in the photoelectric effect, it behaves like a
shower of photons. Now we have just the opposite
state of affairs for electrons. We accustomed ourselves
to the idea that electrons are particles, elementary-
quanta of electricity and matter. Their charge and mass
were investigated. If there is any truth in de Broglie’s
idea, then there must be some phenomena in which
matter reveals its wave-like character. At first, this con-
clusion, reached by following the acoustical analogy,
seems strange and incomprehensible. How can a mov-
ing corpuscle have anything to do with a wave? But
this is not the first time we have faced a difficulty of
this kind in physics. We met the same problem in the
domain of light phenomena.

Fundamental ideas play the most essential role in
forming a physical theory. Books on physics are full
of complicated mathematical formulae. But thought
and ideas, not formulae, are the beginning of every
physical theory. The ideas must later take the mathe-
matical form of a quantitative theory, to make possible
the comparison with experiment. This can be explained
by the example of the problem with which we are now
dealing. The principal guess is that the uniformly mov-
ing electron will behave, in some phenomena, like a
wave. Assume that an electron or a shower of electrons,
provided they all have the same velocity, is moving
uniformly. The mass, charge, and velocity of each in-
dividual electron is known. If we wish to associate in

292

The Evolution of Physics

some way a wave concept with a uniformly moving
electron or electrons, our next question must be: what
is the wave-length? This is a quantitative question and
a more or less quantitative theory must be built up to
answer it. This is indeed a simple matter. The mathe-
matical simplicity of de Broglie’s work, providing an
answer to this question, is most astonishing. At the
time his work was done, the mathematical technique
of other physical theories was very subtle and compli-
cated, comparatively speaking. The mathematics deal-
ing with the problem of waves of matter is extremely
simple and elementary but the fundamental ideas are
deep and far-reaching.

Previously, in the case of light waves and photons,
it was shown that every statement formulated in the
wave language can be translated into the language of
photons or light corpuscles. The same is true for elec-
tronic waves. For uniformly moving electrons, the cor-
puscular language is already known. But every state-
ment expressed in the corpuscular language can be
translated into the wave language, just as in the case
of photons. Two clews laid down the rules of transla-
tion. The analogy between light waves and electronic
waves or photons and electrons is one clew. We try to
use the same method of translation for matter as for
light. The special relativity theory furnished the other
clew. The laws of nature must be invariant with respect
to the Lorentz and not to the classical transformation.
These two clews together determine the wave-length
corresponding to a moving electron. It follows from

Quanta 293

the theory that an electron moving with a velocity of,
say, 1 0,000 miles per second, has a wave-length which
can be easily calculated, and which turns out to lie in
the same region as the X-ray wave-lengths. Thus we
conclude further that if the wave character of matter
can be detected, it should be done experimentally in an
analogous way to that of X rays.

Imagine an electron beam moving uniformly with a
given velocity, or, to use the wave terminology, a
homogeneous electronic wave, and assume that it falls
on a very thin crystal, playing the part of a diffraction
grating. The distances between the diffracting ob-
stacles in the crystal are so small that diffraction for
X rays can be produced. One might expect a similar
effect for electronic waves with the same order of
wave-length. A photographic plate would register this
diffraction of electronic waves passing through the thin
layer of crystal. Indeed, the experiment produces what
is undoubtedly one of the great achievements of the
theory: the phenomenon of diffraction for electronic
waves. The similarity between the diffraction of an
electronic wave and that of an X ray is particularly
marked as seen from a comparison of the patterns in
Plate III. We know that such pictures enable us to
determine the wave-lengths of X rays. The same holds
good for electronic waves. The diffraction pattern
gives the length of a wave of matter and the perfect
quantitative agreement between theory and experiment
confirms the chain of our argument splendidly.

Our previous difficulties are broadened and deep-

294 The Evolution of Physics

ened by this result. This can be made clear by an ex-
ample similar to the one given for a light wave. An
electron shot at a very small hole will bend like a light
wave. Light and dark rings appear on the photo-
graphic plate. There may be some hope of explaining
this phenomenon by the interaction between the elec-
tron and the rim, though such an explanation does not
seem to be very promising. But what about the two
pinholes? Stripes appear instead of rings. How is it
possible that the presence of the other hole completely
changes the effect? The electron is indivisible and can,
it would seem, pass through only one of the two holes.
How could an electron passing through a hole possibly
know that another hole has been made some distance
away?

We asked before: what is light? Is it a shower of cor-
puscles or a wave? We now ask: what is matter, what
is an electron? Is it a particle or a wave? The electron
behaves like a particle when moving in an external
electric or magnetic field. It behaves like a wave when
diffracted by a crystal. With the elementary quanta of
matter we came across the same difficulty that we met
with in the light quanta. One of the most fundamental
questions raised by recent advance in science is how
to reconcile the two contradictory views of matter and
wave. It is one of those fundamental difficulties which,
once formulated, must lead, in the long run, to scien-
tific progress. Physics has tried to solve this problem.
The future must decide whether the solution sug-
gested by modem physics is enduring or temporary.

Quanta

2 95

PROBABILITY WAVES

If, according to classical mechanics, we know the
position and velocity of a given material point and also
what external forces are acting, we can predict, from
the mechanical laws, the whole of its future path. The
sentence: “The material point has such-and-such posi-
tion and velocity at such-and-such an instant,” has a
definite meaning in classical mechanics. If this state-
ment were to lose its sense, our argument (p. 32) about
foretelling the future path would fail.

In the early nineteenth century, scientists wanted to
reduce all physics to simple forces acting on material
particles that have definite positions and velocities at
any instant. Let us recall how we described motion
when discussing mechanics at the beginning of our
journey through the realm of physical problems. We
drew points along a definite path showing the exact
positions of the body at certain instants and then tan-
gent vectors showing the direction and magnitude of
the velocities. This was both simple and convincing.
But it cannot be repeated for our elementary quanta of
matter, that is electrons, or for quanta of energy, that
is photons. We cannot picture the journey of a photon
or electron in the way we imagined motion in classical
mechanics. The example of the two pinholes shows this
clearly. Electron and photon seem to pass through the
two holes. It is thus impossible to explain the effect by
picturing the path of an electron or a photon in the old
classical way.

296 The Evolution of Physics

We must, of course, assume the presence of ele-
mentary actions, such as the passing of electrons or
photons through the holes. The existence of elementary
quanta of matter and energy cannot be doubted. But
the elementary laws certainly cannot be formulated by
specifying positions and velocities at any instant in the
simple manner of classical mechanics.

Let us, therefore, try something different. Let us
continually repeat the same elementary processes. One
after the other, the electrons are sent in the direction of
the pinholes. The word “electron” is used here for the
sake of definiteness; our argument is also valid for
photons.

The same experiment is repeated over and over again
in exactly the same way; the electrons all have the same
velocity and move in the direction of the two pinholes.
It need hardly be mentioned that this is an idealized
experiment which cannot be carried out in reality but
may well be imagined. We cannot shoot out single
photons or electrons at given instants, like bullets from
a gun.

The outcome of repeated experiments must again be
dark and light rings for one hole and dark and light
stripes for two. But there is one essential difference. In
the case of one individual electron, the experimental
result was incomprehensible. It is more easily under-
stood when the experiment is repeated many times. We
can now say: light stripes appear where many electrons
fall. The stripes become darker at the place where
fewer electrons are falling. A completely dark spot

Quanta 297

means that there are no electrons. We are not, of
course, allowed to assume that all the electrons pass
through one of the holes. If this were so it could not
make the slightest difference whether or not the other
is covered. But we already know that covering the
second hole does make a difference. Since one particle
is indivisible we cannot imagine that it passes through
both the holes. The fact that the experiment was re-
peated many times points to another way out. Some of
the electrons may pass through the first hole and others
through the second. We do not know why individual
electrons choose particular holes, but the net result of
repeated experiments must be that both pinholes par-
ticipate in transmitting the electrons from the source
to the screen. If we state only what happens to the
crowd of elecrons when the experiment is repeated,
not bothering about the behavior of individual parti-
cles, the difference between the ringed and the striped
pictures becomes comprehensible. By the discussion of
a sequence of experiments a new idea was born, that
of a crowd with the individuals behaving in an unpre-
dictable way. We cannot foretell the course of one
single electron, but we can predict that, in the net re-
sult, the light and dark stripes will appear on the
screen.

Let us leave quantum physics for the moment.

We have seen in classical physics that if we know
the position and velocity of a material point at a certain
instant and the forces acting upon it, we can predict its
future path. We also saw how the mechanical point of

298 The Evolution of Physics

view was applied to the kinetic theory of matter. But
in this theory a new idea arose from our reasoning. It
will be helpful in understanding later arguments to
grasp this idea thoroughly.

There is a vessel containing gas. In attempting to
trace the motion of every particle one would have to
commence by finding the initial states, that is, the
initial positions and velocities of all the particles. Even
if this were possible, it would take more than a human
lifetime to set down the result on paper, owing to the
enormous number of particles which would have to be
considered. If one then tried to employ the known
methods of classical mechanics for calculating the final
positions of the particles, the difficulties would be
insurmountable. In principle, it is possible to use the
method applied for the motion of planets, but in prac-
tice this is useless and must give way to the method of
statistics. This method dispenses with any exact knowl-
edge of initial states. We know less about the system at
any given moment and are thus less able to say any-
thing about its past or future. We become indifferent
to the fate of the individual gas particles. Our problem
is of a different nature. For example: we do not ask,
“What is the speed of every particle at this moment?”
But we may ask: “How many particles have a speed
between 1000 and 1100 feet per second?” We care
nothing for individuals. What we seek to determine
are average values typifying the whole aggregation. It
is clear that there can be some point in a statistical

Quanta 299

method of reasoning only when the system consists of
a large number of individuals.

By applying the statistical method we cannot fore-
tell the behavior of an individual in a crowd. We can
only foretell the chance, the probability, that it will
behave in some particular manner. If our statistical
laws tell us that one-third of the particles have a speed
between 1000 and 1 100 feet per second, it means that
by repeating our observations for many particles, we
shall really obtain this average, or in other words, that
the probability of finding a particle within this limit is
equal to one-third.

Similarly, to know the birth rate of a great com-
munity does not mean knowing whether any particular
family is blessed with a child. It means a knowledge of
statistical results in which the contributing personalities
play no role.

By observing the registration plates of a great many
cars we can soon discover that one-third of their num-
bers are divisible by three. But we cannot foretell
whether the car which will pass in the next moment
will have this property. Statistical laws can be applied
only to big aggregations, but not to their individual
members.

We can now return to our quantum problem.

The laws of quantum physics are of a statistical char-
acter. This means: they concern not one single system
but an aggregation of identical systems; they cannot be
verified by measurement of one individual, but only by
a series of repeated measurements.

3 00 The Evolution of Physics

Radioactive disintegration is one of the many events
for which quantum physics tries to formulate laws
governing the spontaneous transmutation from one ele-
ment to another. We know, for example, that in 1600
years half of one gram of radium will disintegrate, and
half will remain. We can foretell approximately how
many atoms will disintegrate during the next half-hour,
but we cannot say, even in our theoretical descrip-
tions, why just these particular atoms are doomed.
According to our present knowledge, we have no
power to designate the individual atoms condemned to
disintegration. The fate of an atom does not depend on
its age. There is not the slightest trace of a law govern-
ing their individual behavior. Only statistical laws can
be formulated, laws governing large aggregations of
atoms.

Take another example. The luminous gas of some
element placed before a spectroscope shows lines of
definite wave-length. The appearance of a discontinu-
ous set of definite wave-lengths is characteristic of the
atomic phenomena in which the existence of elemen-
tary quanta is revealed. But there is still another aspect
of this problem. Some of the spectrum lines are very
distinct, others are fainter. A distinct line means that a
comparatively large number of photons belonging to
this particular wave-length are emitted; a faint line
means that a comparatively small number of photons
belonging to this wave-length are emitted. Theory
again gives us statements of a statistical nature only.
Every line corresponds to a transition from higher to

Quanta 301

lower energy level. Theory tells us only about the
probability of each of these possible transitions, but
nothing about the actual transition of an individual
atom. The theory works splendidly because all these
phenomena involve large aggregations and not single
individuals.

It seems that the new quantum physics resembles
somewhat the kinetic theory of matter, since both are
of a statistical nature and both refer to great aggrega-
tions. But this is not so! In this analogy an understanding
not only of the similarities but also of the differences
is most important. The similarity between the kinetic
theory of matter and quantum physics lies chiefly in
their statistical character. But what are the differences?

If we wish to know how many men and women over
the age of twenty live in a city, we must get every citi-
zen to fill out a form under the headings: “male,”
“female,” and “age.” Provided every answer is correct,
we can obtain, by counting and segregating them, a
result of a statistical nature. The individual names and
addresses on the forms are of no account. Our statis-
tical view is gained by the knowledge of individual
cases. Similarly, in the kinetic theory of matter, we
have statistical laws governing the aggregation, gained
on the basis of individual laws.

But in quantum physics the state of affairs is entirely
different. Here the statistical laws are given immedi-
ately. The individual laws are discarded. In the exam-
ple of a photon or an electron and two pinholes we
have seen that we cannot describe the possible motion

302

The Evolution of Physics

of elementary particles in space and time as we did in
classical physics. Quantum physics abandons individual
laws of elementary particles and states directly the sta-
tistical laws governing aggregations. It is impossible, on
the basis of quantum physics, to describe positions and
velocities of an elementary particle or to predict its
future path as in classical physics. Quantum physics
deals only with aggregations, and its laws are for
crowds and not for individuals.

It is hard necessity and not speculation or a desire for
novelty which forces us to change the old classical
view. The difficulties of applying the old view have
been outlined for one instance only, that of diffraction
phenomena. But many others, equally convincing,
could be quoted. Changes of view are continually
forced upon us by our attempts to understand reality.
But it always remains for the future to decide whether
we chose the only possible way out and whether or
not a better solution of our difficulties could have been
found.

We have had to forsake the description of individual
cases as objective happenings in space and time; we
have had to introduce laws of a statistical nature. These
are the chief characteristics of modem quantum
physics.

Previously, when introducing new physical realities,
such as the electromagnetic and gravitational field, we
tried to indicate in general terms the characteristic fea-
tures of the equations through which the ideas have
been mathematically formulated. We shall now do the

Quanta 303

same with quantum physics, referring only very briefly
to the work of Bohr, De Broglie, Schrodinger, Heisen-
berg, Dirac and Born.

Let us consider the case of one electron. The elec-
tron may be under the influence of an arbitrary foreign
electromagnetic field, or free from all external in-
fluences. It may move, for instance, in the field of an
atomic nucleus or it may diffract on a crystal. Quan-
tum physics teaches us how to formulate the mathe-
matical equations for any of these problems.

We have already recognized the similarity between
an oscillating cord, the membrane of a drum, a wind
instrument, or any other acoustical instrument on the
one hand, and a radiating atom on the other. There is
also some similarity between the mathematical equa-
tions governing the acoustical problem and those gov-
erning the problem of quantum physics. But again the
physical interpretation of the quantities determined in
these two cases is quite different. The physical quan-
tities describing the oscillating cord and the radiating
atom have quite a different meaning, despite some
formal likeness in the equations. In the case of the cord,
we ask about the deviation of an arbitrary point from
its normal position at an arbitrary moment. Knowing
the form of the oscillating cord at a given instant, we
know everything we wish. The deviation from the
normal can thus be calculated for any other moment
from the mathematical equations for the oscillating
cord. The fact that some definite deviation from the
normal position corresponds to every point of the cord

304 The Evolution of Physics

is expressed more rigorously as follows: for any in-
stant, the deviation from the normal value is a function
of the co-ordinates of the cord. All points of the cord
form a one-dimensional continuum, and the deviation
is a function defined in this one-dimensional con-
tinuum, to be calculated from the equations of the
oscillating cord.

Analogously, in the case of an electron a certain
function is determined for any point in space and for
any moment. We shall call this function the probability
wave. In our analogy the probability wave corresponds
to the deviation from the normal position in the acous-
tical problem. The probability wave is, at a given in-
stant, a function of a three-dimensional continuum,
whereas, in the case of the cord the deviation was, at a
given moment, a function of the one-dimensional con-
tinuum. The probability wave forms the catalogue of
our knowledge of the quantum system under consid-
eration and will enable us to answer all sensible statis-
tical questions concerning this system. It does not tell
us the position and velocity of the electron at any mo-
ment because such a question has no sense in quantum
physics. But it will tell us the probability of meeting
the electron on a particular spot, or where we have the
greatest chance of meeting an electron. The result does
not refer to one, but to many repeated measurements.
Thus the equations of quantum physics determine the
probability wave just as Maxwell’s equations determine
the electromagnetic field and the gravitational equa-
tions determine the gravitational field. The laws of

Quanta 305

quantum physics are again structure laws. But the
meaning of physical concepts determined by these
equations of quantum physics is much more abstract
than in the case of electromagnetic and gravitational
fields; they provide only the mathematical means of an-
swering questions of a statistical nature.

So far we have considered the electron in some ex-
ternal field. If it were not the electron, the smallest
possible charge, but some respectable charge containing
billions of electrons, we could disregard the whole
quantum theory and treat the problem according to
our old pre-quantum physics. Speaking of currents in
a wire, of charged conductors, of electromagnetic
waves, we can apply our old simple physics contained
in Maxwell’s equations. But we cannot do this when
speaking of the photoelectric effect, intensity of spec-
tral lines, radioactivity, diffraction of electronic waves
and many other phenomena in which the quantum
character of matter and energy is revealed. We must
then, so to speak, go one floor higher. Whereas in
classical physics we spoke of positions and velocities of
one particle, we must now consider probability waves,
in a three-dimensional continuum corresponding to
this one-particle problem.

Quantum physics gives its own prescription for
treating a problem if we have previously been taught
how to treat an analogous problem from the point of
view of classical physics.

For one elementary particle, electron or photon, we
have probability waves in a three-dimensional con-

30 6 The Evolution of Physics

tinuum, characterizing the statistical behavior of the
system if the experiments are often repeated. But what
about the case of not one but two interacting particles,
for instance, two electrons, electron and photon, or
electron and nucleus? We cannot treat them separately
and describe each of them through a probability wave
in three dimensions, just because of their mutual inter-
action. Indeed, it is not very difficult to guess how to
describe in quantum physics a system composed of two
interacting particles. We have to descend one floor, to
return for a moment to classical physics. The position
of two material points in space, at any moment, is char-
acterized by six numbers, three for each of the points.
All possible positions of the two material points form a
six-dimensional continuum and not a three-dimensional
one as in the case of one point. If we now again ascend
one floor, to quantum physics, we shall have probabil-
ity waves in a six-dimensional continuum and not in a
three-dimensional continuum as in the case of one par-
ticle. Similarly, for three, four, and more particles the
probability waves will be functions in a continuum of
nine, twelve, and more dimensions.

This shows clearly that the probability waves are
more abstract than the electromagnetic and gravita-
tional field existing and spreading in our three-dimen-
sional space. The continuum of many dimensions forms
the background for the probability waves, and only
for one particle does the number of dimensions equal
that of physical space. The only physical significance
of the probability wave is that it enables us to answer

ft

Quanta 307

sensible statistical questions in the case of many par-
ticles as well as of one. Thus, for instance, for one
electron we could ask about the probability of meeting
an electron in some particular spot. For two particles
our question could be: what is the probability of meet-
ing the two particles at two definite spots at a given
instant?

Our first step away from classical physics was aban-
doning the description of individual cases as objective
events in space and time. We were forced to apply the
statistical method provided by the probability waves.
Once having chosen this way, we are obliged to go
further toward abstraction. Probability waves in many
dimensions corresponding to the many-particle prob-
lem must be introduced.

Let us, for the sake of briefness, call everything ex-
cept quantum physics, classical physics. Classical and
quantum physics differ radically. Classical physics aims
at a description of objects existing in space, and the
formulation of laws governing their changes in time.
But the phenomena revealing the particle and wave
nature of matter and radiation, the apparently statis-
tical character of elementary events such as radioactive
disintegration, diffraction, emission of spectral lines,
and many others, forced us to give up this view. Quan-
tum physics does not aim at the description of indi-
vidual objects in space and their changes in time. There
is no place in quantum physics for statements such as:
“This object is so-and-so, has this-and-this property.”
Instead we have statements of this kind: “There is

308 The Evolution of Physics

such-and-such a probability that the individual object
is so-and-so and has this-and-this property.” There is
no place in quantum physics for laws governing the
changes in time of the individual object. Instead, we
have laws governing the changes in time of the prob-
ability. Only this fundamental change, brought into
physics by the quantum theory, made possible an ade-
quate explanation of the apparently discontinuous and
statistical character of events in the realm of phenom-
ena in which the elementary quanta of matter and
radiation reveal their existence.

Yet new, still more difficult problems arise which
have not been definitely settled as yet. We shall men-
tion only some of these unsolved problems. Science is
not and will never be a closed book. Every important
advance brings new questions. Every development re-
veals, in the long run, new and deeper difficulties.

We already know that in the simple case of one or
many particles we can rise from the classical to the
quantum description, from the objective description of
events in space and time to probability waves. But we
remember the all-important field concept in classical
physics. How can we describe interaction between ele-
mentary quanta of matter and field? If a probability
wave in thirty dimensions is needed for the quantum
description of ten particles, then a probability wave
with an infinite number of dimensions would be needed
for the quantum description of a field. The transition
from the classical field concept to the corresponding
problem of probability waves in quantum physics is a

Quanta 309

very difficult step. Ascending one floor is here no easy
task and all attempts so far made to solve the problem
must be regarded as unsatisfactory. There is also one
other fundamental problem. In all our arguments about
the transition from classical physics to quantum physics
we used the old prerelativistic description in which
space and time are treated differently. If, however, we
try to begin from the classical description as proposed
by the relativity theory, then our ascent to the quan-
tum problem seems much more complicated. This is
another problem tackled by modem physics, but s till
far from a complete and satisfactory solution. There is
still a further difficulty in forming a consistent physics
for heavy particles, constituting the nuclei. In spite of
the many experimental data and the many attempts to
throw light on the nuclear problem, we are still in the
dark about some of the most fundamental questions in
this domain.

There is no doubt that quantum physics explained a
very rich variety of facts, achieving, for the most part,
splendid agreement between theory and observation.
The new quantum physics removes us still further
from the old mechanical view, and a retreat to the
former position seems, more than ever, unlikely. But
there is also no doubt that quantum physics must still
be based on the two concepts: matter and field. It is,
in this sense, a dualistic theory and does not bring our
old problem of reducing everything to the field con-
cept even one step nearer realization.

Will the further development be along the line

3 io

The Evolution of Physics

chosen in quantum physics, or is it more likely that
new revolutionary ideas will be introduced into phys-
ics? Will the road of advance again make a sharp turn,
as it has so often done in the past?

During the last few years all the difficulties of quan-
tum physics have been concentrated around a few
principal points. Physics awaits their solution impa-
tiently. But there is no way of foreseeing when and
where the clarification of these difficulties will be
brought about.

PHYSICS AND REALITY

What are the general conclusions which can be
drawn from the development of physics indicated here
in a broad outline representing only the most funda-
mental ideas?

Science is not just a collection of laws, a catalogue of
unrelated facts. It is a creation of the human mind,
with its freely invented ideas and concepts. Physical
theories try to form a picture of reality and to estab-
lish its connection with the wide world of sense im-
pressions. Thus the only justification for our mental
structures is whether and in what way our theories
form such a link.

We have seen new realities created by the advance
of physics. But this chain of creation can be traced
back far beyond the starting point of physics. One of
the most primitive concepts is that of an object. The
concepts of a tree, a horse, any material body, are crea-
tions gained on the basis of experience, though the im-

Quanta 3 1 1

pressions from which they arise are primitive in com-
parison with the world of physical phenomena. A cat
teasing a mouse also creates, by thought, its own primi-
tive reality. The fact that the cat reacts in a similar way
toward any mouse it meets shows that it forms con-
cepts and theories which are its guide through its own
world of sense impressions.

“Three trees” is something different from “two
trees.” Again “two trees” is different from “two
stones.” The concepts of the pure numbers 2,3,4...,
freed from the objects from which they arose, are
creations of the thinking mind which describe the re-
ality of our world.

The psychological subjective feeling of time enables
us to order our impressions, to state that one event
precedes another. But to connect every instant of time
with a number, by the use of a clock, to regard time as
a one-dimensional continuum, is already an invention.
So also are the concepts of Euclidean and non-Euclid-
ean geometry, and our space understood as a three-
dimensional continuum.

Physics really began with the invention of mass,
force, and an inertial system. These concepts are all
free inventions. They led to the formulation of the
mechanical point of view. For the physicist of the
early nineteenth century, the reality of our outer
world consisted of particles with simple forces acting
between them and depending only on the distance. He
tried to retain as long as possible his belief that he
would succeed in explaining all events in nature by

3 12

The Evolution of Physics

these fundamental concepts of reality. The difficulties
connected with the deflection of the magnetic needle,
the difficulties connected with the structure of the
ether, induced us to create a more subtle reality. The
important invention of the electromagnetic field ap-
pears. A courageous scientific imagination was needed
to realize fully that not the behavior of bodies, but
the behavior of something between them, that is, the
field, may be essential for ordering and understanding
events.

Later developments both destroyed old concepts
and created new ones. Absolute time and the inertial
co-ordinate system were abandoned by the relativity
theory. The background for all events was no longer
the one-dimensional time and the three-dimensional
space continuum, but the four-dimensional time-space
continuum, another free invention, with new transfor-
mation properties. The inertial co-ordinate system was
no longer needed. Every co-ordinate system is equally
suited for the description of events in nature.

The quantum theory again created new and essential
features of our reality. Discontinuity replaced con-
tinuity. Instead of laws governing individuals, prob-
ability laws appeared.

The reality created by modem physics is, indeed, far
removed from the reality of the early days. But the aim
of every physical theory still remains the same.

With the help of physical theories we try to find our
way through the maze of observed facts, to order and
understand the world of our sense impressions. We

Quanta 3 1 3

want the observed facts to follow logically from our
concept of reality. Without the belief that it is possible
to grasp the reality with our theoretical constructions,
without the belief in the inner harmony of our world,
there could be no science. This belief is and always will
remain the fundamental motive for all scientific crea-
tion. Throughout all our efforts, in every dramatic
struggle between old and new views, we recognize the
eternal longing for understanding, the ever-firm belief
in the harmony of our world, continually strengthened
by the increasing obstacles to comprehension.

We Summarize:

Again the rich variety of facts in the realm of atomic
phenomena forces us to invent new physical concepts.
Matter has a granular structure; it is composed of elemen-
tary particles, the elementary quanta of matter. Thus , the
electric charge has a granular structure and— most impor-
tant from the point of view of the quantum theory— so has
energy. Photons are the energy quanta of which light is
composed.

Is light a wave or a shower of photons? Is a beam of
electrons a shower of elementary particles or a wave?
These fundamental questions are forced upon physics by
experiment. In seeking to answer them we have to abandon
the description of atomic events as happenings in space and
time, we have to retreat still further from the old mechan-
ical view. Quantum physics formulates laws governing
crowds and not individuals. Not properties but probabili-
ties are described, not laws disclosing the future of systems
are formulated, but laws governing the changes in time of
the probabilities and relating to great congregations of
individuals.

INDEX

Index

Absolute motion, 180, 224
Aristotle, 6

Black, 39, 40, ji

Bohr, 283, 303

Bom, 303

Brown, 63, 64

Brownian movement, 63-67

Caloric, 43

Change in velocity, 10, 18, 23-24,
28

Classical transformation, 171
Conductors, 74
Constant of the motion, 49
Continuum:

one-dimensional, 21:
two-dimensional, 21 1
three-dimensional, 212
four-dimensional, 219
Co-ordinate of a point, 168
Co-ordinate system, 162, 163
Copernicus, 161, 223, 224
Corpuscles of light, 99, ioo, 275
Coulomb, 79, 86
Crucial experiments, 44-4J
Crystal, 285
CS, 163
Current, 88
induced, 142

De Broglie, 287, 290, 303
Democritus, 56
Diffraction:

of electronic wave, 293

Diffraction— ( Continued )
of light, 1 19
of X rays, 286
Dipole:
electric, 84
magnetic, 8j
Dirac, 303
Dispersion, 102, 117
Dynamic picture of motion, 217

Electric:

charge, 80-82
current, 88
potential, 80-82
substances, 74
Electromagnetic :
field, 151

theory of light, 137
wave, 154

Electronic wave, 292
Electrons, 268
Electroscope, 71
Elementary:

magnetic dipoles, 85
particles, 206
quantum, 264
Elements of a battery, 88
Energy:
kinetic, 49, 50
level, 282
mechanical, 31
potential, 49, 50

Ether, 112, 113, 120, 123-126, 172,
173, 176, 179, 180-184

317

Index

18

Faraday, 129, 142
Field, 131
representation, 131
static, 141

structure of, 149, 152
Fizeau, 96

Frame of reference, 163
Fresnel, 118
Force, 11, 19, 24, 28
lines, 130
matter, 56

Galilean relativity principle, 165
Galileo, 5, 7, 8, 9, 39, 56, 94, 9 j,
96

Galvani, 88
Generalization, 20
General relativity, 36, 225
Gravitational mass, 36, 227, 230

Heat, 38, 41, 42
capacity, 41
energy, 50-55
specific, 41
substance, 42, 43
Heisenberg, 303
Helmholtz, 58, 59
Hertz, 129, 156
Huygens, no, in

Induced current, 142
Inertial mass, 36, 227, 230
system, 166, 220, 221
system, local, 228, 229
Insulators, 71, 74
Invariant, 170

Joule, 51, 52, 53

Kinetic theory, 59-67

Law of gravitation, 30
of inertia, 8, 160
of motion, 31
Leibnitz, 25

Light, bending in gravitational
field, 234, 253
homogeneous, 103
quanta, 275
substance, 102-104
white, 101

Lorentz transformation, 198-202

Mass, 34
energy, 208
of one electron, 270
of one hydrogen atom, 2 66
of one hydrogen molecule,
67, 265

Matter-energy, 54
field, 256
Maxwell, 129

Maxwell’s equations, 148, 149,
Ho, 153
Mayer, 51

Mechanical equivalent of heat,
54

Mechanical view, 59, 87, 92, 120,
I2 4, iJ7
Mercury, 253
Metric properties, 246
Michelson, 97, 183
Molecules, 59
number of, 66
Morley, 183

Newton, 5, 8, 9, 25, 79, 92, 100,
101

Nodes, 288
Nuclear physics, 272
Nucleus, 271

Oersted, 90, 91

Index

3i9

Photoelectric effect, 273
Photons, 275
ultraviolet, 284
Planck, 273
Pole, magnetic, 83
Principia, 11
Probability, 299
wave, 304
Ptolemy, 223, 224

Radioactive disintegration, 300
matter, 206
Radium, 206
Rate of exchange, 32
Rectilinear motion, 12
propagation of light, 97, 99,
120

Reflection of light, 99
Refraction, 98, 99, 113, 116
Relative uniform motion, 180
Relativity, 186
general, 36, 223
special, 223
Rest mass, 205
Roemer, 96
Rowland, 92
Rumford, 43, 47, 31
Rutherford, 272

Schrodinger, 287, 303
Sodium, 103
Solenoid, 136
Special relativity, 223
Spectral lines, 280
Spectroscope, 281

Spectrum, visible, 102, 284
Static picture of motion, 217
Statistics, 298
Synchronized clocks, 191

Temperature, 38-40
Test body, 130
Thomson, J. J., 268
Tourmaline crystal, 12 1
Transformation laws, 169
Two New Sciences, 10, 94

Uniform motion, 9

Vectors, 12-19

Velocity of electromagnetic
wave, 133
of light, 97
vector, 21
Volta, 88, 89
Voltaic battery, 88

Wave, 104
length, 106, n 7
longitudinal, 108, 121
plane, no
spherical, 109
standing, 288
theory of light, no
transverse, 108, 12:
velocity, 106

Weightless substances, 43, 79
X rays, 284-285
Young, 118

About the Authors

Albert Einstein was born in 18-19 at Ulm, in southern
Germany. He studied at the Polytechnic in Zurich and
from 1902 to 1909 worked as an engineer in the Berne
Patent Office. Between 1909 and 1914 he served as Pro-
fessor of Physics at the Universities of Zurich and Prague,
and at the Polytechnic of Zurich. The year the World War
broke out, Professor Einstein became a member of the
Prussian Academy of Sciences, where he remained until
1932, when he left Germany to become a professor at the
Institute for Advanced Study in Princeton, New Jersey.

Leopold Infeld was born in 1898 at Cracow, which then
belonged to Austria-Hungary (now Poland) and is one of
the most ancient university towns in Europe. He studied
at the Universities of Cracow and Berlin, and in 1 930 be-
came a lecturer at the Polish University of Lwow
(formerly Lemberg). He spent the years 1933 to 1933 in
Cambridge, England, as a Fellow of the Rockefeller Foun-
dation, and in 1936 joined the Institute for Advanced
Study at Princeton, New Jersey.

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